[seqfan] Re: definition of A002848
N. J. A. Sloane
njas at research.att.com
Thu Feb 11 23:07:44 CET 2010
Richard, thanks for noticing that typo!
The definition should have read
%N A002848 a(n) = number of partitions of a subset of {1, 2, ..., n} into triples, as in A002849, with the property that n is in one of the triples.
referring to
%N A002849 Number of partitions of a subset of {1, 2, ..., n} into triples (X,Y,Z) each satisfying X+Y=Z, with the maximal possible number of such triples.
Both are based on
%D A002849 R. K. Guy, ``Sedlacek's Conjecture on Disjoint Solutions of x+y= z,'' Univ. Calgary, Dept. Mathematics, Research Paper No. 129, 1971.
and
%D A002849 R. K. Guy, ``Sedlacek's Conjecture on Disjoint Solutions of x+y= z,'' in Proc. Conf. Number Theory. Pullman, WA, 1971, pp. 221-223.
And we also have
%N A108235 Number of partitions of {1,2,...,3n} into n triples (X,Y,Z) each satisfying X+Y=Z.
%C A108235 It is known that a(n) = 0 unless n == 0 or 1 mod 4. For n == 0 or 1 mod 4, a(n) = A002849(3n). See A002849 for references and further information.
Incidentally, I just added another from the same stable:
%I A161826
%S A161826 1,1,3,2,6,1,6,1,5,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,
%T A161826 1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,
%U A161826 4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4
%N A161826 Number of maximal vertex-independent sets in the hypergraph with nodes V = {1, 2, ..., n} and "edges" consisting of the triples (X,Y,Z) with X<Y<Z and X+Y=Z.
%C A161826 A subset S of V is vertex-independent if there is no edge (X,Y,Z) with X, Y, Z all in S.
%Y A161826 J. Sedlacek, On a set system, Annals New York Acad. Sci., 175 (No. 1, 1970), 329-330.
%Y A161826 Cf. A002848, A002849, A108235.
%O A161826 1,3
%K A161826 nonn
%F A161826 a(2k)=1, a(2k+1)=4 for k >= 5.
%A A161826 N. J. A. Sloane (njas(AT)research.att.com), Feb 10 2010
Best regards
Neil
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