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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 (list; table; graph; refs; listen; history; text; internal format)
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: A252055 A324144 A320836 * A022881 A093201 A067613

Adjacent sequences:  A097564 A097565 A097566 * A097568 A097569 A097570

KEYWORD

easy,nonn,tabl

AUTHOR

Wouter Meeussen, Aug 28 2004

STATUS

approved

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Last modified March 21 13:51 EDT 2019. Contains 321370 sequences. (Running on oeis4.)