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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'. 0
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.

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

Sequence in context: A140397 A120614 A252055 * 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 25 05:35 EDT 2017. Contains 284036 sequences.