# %R references

N. J. A. Sloane njas at research.att.com
Sat Dec 11 05:28:38 CET 1999

```Here is another one that got filled in:

%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.
%D A002050 J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk
Aktuarietidskrift, Vol. 11, pp. 75-97, 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 - exp(x)) / (1 - 2*exp(-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

Now just two remain:

%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 A002817 M4141 N1718
%S A002817 1,6,21,55,120,231,406,666,1035,1540,2211,3081,4186,5565,7260,9316,
%T A002817 11781,14706,18145,22155,26796,32131,38226,45150,52975,61776,71631,826
21
%N A002817 Doubly triangular numbers: C(n+2,2)+3C(n+3,4).
*** %R A002817 Transactions of the Cambridge Philosophical Society, Vol. 9, p. 4
77, 1856.
%D A002817 D. M. Jackson and G. H. J. van Rees, The enumeration of generalized d
ouble 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, 1159-11
89.
%O A002817 0,2
%A A002817 njas
%K A002817 nonn,easy,nice

Neil Sloane

```