

A097567


T(n,k)= count of partitions p such that Abs( Odd(p)Odd(p') ) = k, where p' is the transpose of p and Odd(p) counts the odd elements in p. Related to Stanley's 'f'.


1



1, 1, 0, 0, 0, 2, 1, 0, 2, 0, 3, 0, 0, 0, 2, 3, 0, 2, 0, 2, 0, 1, 0, 8, 0, 0, 0, 2, 3, 0, 8, 0, 2, 0, 2, 0, 10, 0, 2, 0, 8, 0, 0, 0, 2, 10, 0, 8, 0, 8, 0, 2, 0, 2, 0, 4, 0, 26, 0, 2, 0, 8, 0, 0, 0, 2, 10, 0, 26, 0, 8, 0, 8, 0, 2, 0, 2, 0, 27, 0, 10, 0, 28, 0, 2, 0, 8, 0, 0, 0, 2, 27, 0, 26, 0, 28, 0, 8, 0, 8
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OFFSET

0,6


COMMENTS

Table starts {1}, {1,0}, {0,0,2}, {1,0,2,0}, {3,0,0,0,2}, .. where the odd columns are 0. Row sums are A000041 by definition.


LINKS

Table of n, a(n) for n=0..99.
George E. Andrews, On a Partition Function of Richard Stanley, The Electronic Journal of Combinatorics, Volume 11, Issue 2 (20046) (The Stanley Festschrift volume), Research Paper #R1.
Andrew V. Sills, A Combinatorial proof of a partition identity of Andrews and Stanley, International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 47, Pages 24952501.


MATHEMATICA

Table[par=Partitions[n]; Table[Count[par, q_/; Abs[Count[q, _?OddQ]Count[TransposePartition[q], _?OddQ]]===k], {k, 0, n}], {n, 0, 16}]


CROSSREFS

Cf. A097566.
Sequence in context: A324144 A320836 A351977 * A022881 A328748 A093201
Adjacent sequences: A097564 A097565 A097566 * A097568 A097569 A097570


KEYWORD

easy,nonn,tabl


AUTHOR

Wouter Meeussen, Aug 28 2004


STATUS

approved



