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, 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

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 (2004-6) (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 2495-2501.

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