references needed

Thu Dec 2 02:06:25 CET 1999

Dear Sequence Fans,                                Dec 1 1999

For the past year I have been replacing all
the old condensed references (in %R) lines by detailed references (in %D lines).
There were originally over 5,000 %R references, but only 10 remain.

If any of you have access to a good library, I would very
much appreciate getting the author's name, the title of the article,
and the full page numbers for the ten %R lines which follow.

(I have marked these lines with ****)

Note that the page referred to is often in the middle
of the article.

Thanks!

Neil Sloane  (njas at research.att.com)

%I A002326 M0936 N0350
%S A002326 1,2,4,3,6,10,12,4,8,18,6,11,20,18,28,5,10,12,36,12,20,14,12,23,21,
%T A002326 8,52,20,18,58,60,6,12,66,22,35,9,20,30,39,54,82,8,28,11,12,10,36,48,30
%N A002326 Multiplicative order of 2 mod 2n+1.
*** %R A002326 Atti del Seminario Matematico e Fisico dell' Universit\`{a} di Modena, Vol. 10, p. 226, 1961.
%D A002326 "On Binal Fractions" by Allan J. C. Cunningham, Math. Gaz., 4 (1908), circa p. 266.
%D A002326 S. W. Golomb, Permutations by cutting and shuffling, SIAM Rev., 3 (1961), 293-297.
%O A002326 0,2
%A A002326 njas
%K A002326 nonn,easy,nice
%p A002326 with(numtheory): f:=n->order(2,2*n+1);

%I A002094 M1383 N0541
%S A002094 2,5,10,25,56,139,338,852
%N A002094 Alcohols with n carbon atoms.
*** %R A002094 Berichte der Deutschen Chemischen Gesellschaft, Vol. 8, p. 1545, 1875.
%O A002094 3,1
%A A002094 njas
%K A002094 nonn

%I A002102 M2265 N0895
%S A002102 1,3,3,1,3,6,3,0,3,6,6,3,1,6,6,0,3,9,6,3,6,6,3,0,3,9,12,4,0,12,6,0,
%T A002102 3,6,9,6,6,6,9,0,6,15,6,3,3,12,6,0,1,9,15,6,6,12,12,0,6,6,6,9,0,12,12,0,3
%N A002102 Nonnegative solutions of x^2 + y^2 + z^2 = n.
*** %R A002102 Proceedings of the National Institute of Sciences of India, Vol. 13, p.  39, 1947.
%D A002102 A. Das and A. C. Melissinos, Quantum Mechanics: A Modern Introduction, Gordon and Breach, 1986, p. 48.
%O A002102 0,2
%A A002102 njas
%K A002102 nonn
%F A002102 Coefficient of q^k in 1/8*(1 + theta_3(0, q))^3, or coefft of q^n in (1+q+q^4+q^9+q^16+q^25+q^36+q^49+q^64+...)^3.

%I A000592 M2324 N0919
%S A000592 1,3,4,6,8,9,11,13,15,17,19,20,22,26,28,30,31,33,35,37,39,41,43,45,
%T A000592 48,50,52,54,56,58,62,64,65,67,69,71,73,75,79,81,83,85,86,90,92,94,96,98
%N A000592 Nonnegative solutions of x^2 + y^2 = z in first n shells.
*** %R A000592 Research Bulletin of the Panjab University, Vol. 20, p. 14, 1952.
%O A000592 0,2
%A A000592 njas
%K A000592 nonn

%I A002902 M2990 N1210
%S A002902 1,3,15,75,363,1767,8463,40695,193983,926943,4404939,20967075,
%T A002902 99421371,471987255,2234455839,10587573027,50060937987,
%U A002902 236865126051
%N A002902 n-step self-avoiding walks on cubic lattice.
*** %R A002902 Proceedings of the Physical Society, Vol. 92, p. 649, 1967.
%D A002902 M. F. Sykes, Self-avoiding walks on the simple cubic lattice, J. Chem. Phys., 39 (1963), 410-411.
%D A002902 M. F. Sykes et al., The asymptotic behaviour of selfavoiding walks and returns on a lattice, J. Phys.  A 5 (1972), 653-660.
%D A002902 A. M. Nemirovsky et al., Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108.
%D A002902 B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p.462.
%O A002902 1,2
%Y A002902 Equals (1/2)*A001412.
%A A002902 njas
%K A002902 nonn,walk,nice

%I A005121 M3649
%S A005121 1,1,4,32,436,9012,262760,10270696,518277560,32795928016,
%T A005121 2542945605432,237106822506952,26173354092593696,3375693096567983232
%N A005121 Ultradissimilarity relations on an n-set.
*** %R A005121 Analysis, Vol. 12, p. 109, 1992.   [Note that there are several journals with this name.]
%D A005121 M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132.
%D A005121 T. Lengyel, On a recurrence involving Stirling numbers, Europ. J. Combin., 5 (1984), 313-321.
%O A005121 1,3
%A A005121 njas
%K A005121 nonn,nice,easy
%H A005121 <a href="http://www.mathsoft.com/asolve/constant/lngy/lngy.html">More information</a>
%Y A005121 Cf. A006541.
%F A005121 a(n)=Sum_{i=1..n-1} N_i(n), where N_k(m)=Sum_{j=k..m-1} Stirling2(m,j)*N_{k-1}(j), m=3..n, k=2..m-1; N_1(2)=N_1(3)=...=N_1(n)=1.

%I A002503 M3840
%S A002503 5,14,27,41,44,65,76,90,109,125,139,152,155,169,186,189,203,
%T A002503 208,209,219,227,230,237,265,275,298,307,311,314,321,324,
%U A002503 329,344,377,413,419,428,434,439,441,449,458,459,467,475
%N A002503 C(2n,n) is divisible by (n+1)^2.
*** %R A002503 Journal of the Indian Mathematical Society, Vol. 18, p. 97, 1929.
%O A002503 0,1
%A A002503 njas, mb
%K A002503 nonn

%I A002050 M3939 N1622
%S A002050 1,5,25,149,1081,9365,94585,1091669,14174521,204495125,3245265145,
%T A002050 56183135189,1053716696761,21282685940885,460566381955705
%N A002050 Simplices in barycentric subdivision of n-simplex.
*** %R A002050 Skandinavisk Aktuarietidskrift, Vol. 11, p. 95, 1928.
%D A002050 G. J. Simmons, A combinatorial problem associated with a family of combination locks, Math. Mag., 37 (1964), 127-132 (but there are errors).
%O A002050 0,2
%F A002050 E.g.f.: (1 - e^x ) / (1 - 2 e^-x ).
%A A002050 njas
%H A002050 <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=149">ECS 149</a>
%K A002050 nonn,easy,nice

%I A002817 M4141 N1718
%S A002817 1,6,21,55,120,231,406,666,1035,1540,2211,3081,4186,5565,7260,9316,
%T A002817 11781,14706,18145,22155,26796,32131,38226,45150,52975,61776,71631,82621
%N A002817 Doubly triangular numbers: C(n+2,2)+3C(n+3,4).
*** %R A002817 Transactions of the Cambridge Philosophical Society, Vol. 9, p. 477, 1856.
%D A002817 D. M. Jackson and G. H. J. van Rees, The enumeration of generalized double stochastic nonnegative integer square matrices, SIAM J. Comput., 4 (1975), 474-477.
%D A002817 Good, I. J.; On the application of symmetric Dirichlet distributions and their mixtures to contingency tables. Ann. Statist. 4 (1976), no. 6, 1159-1189.
%O A002817 0,2
%A A002817 njas
%K A002817 nonn,easy,nice
%p A002817 (1/8)*(n+1)*(n+2)*(n^2+3*n+4);

%I A002921 M4866 N2081
%S A002921 1,12,132,1404,14652,151116,1546332,15734460,159425580,1609987708,
%T A002921 16215457188,162961837500,1634743178420
%N A002921 Susceptibility series for f.c.c. lattice.
*** %R A002921 Solid State Physics (Journal of Physics C), Vol. 3, p. 268, 1970.
%D A002921 M. E. Fisher and R. J. Burford, Theory of critical point scattering and correlations I: the Ising model, Phys. Rev. 156 (1967), 583-621.
%D A002921 M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, High temperature series for the susceptibility of the Ising model, II. Three dimensional lattices, J. Phys. A 5 (1972) 640-652.
%D A002921 C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 381.
%O A002921 0,2
%A A002921 njas
%K A002921 nonn,nice

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