A305023 Number of triples (p,q,r) of partitions such that p is a partition of n and r <= q <= p (by diagram containment).

1, 3, 12, 34, 100, 246, 630, 1433, 3298, 7124, 15283, 31358, 64100, 126406, 247587, 472864, 895548, 1661690, 3059734, 5538991, 9950980, 17631398, 31004004, 53878023, 92979904, 158806852, 269448833, 453099946, 757152246, 1255180557, 2068707378, 3385065586

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Eric Weisstein's World of Mathematics, Ferrers Diagram

Wikipedia, Ferrers diagram

Example

a(0) = 1: ((),(),()).
a(1) = 3: (1,(),()), (1,1,()), (1,1,1).
a(2) = 12: (11,(),()), (11,1,()), (11,1,1), (11,11,()), (11,11,1), (11,11,11), (2,(),()), (2,1,()), (2,1,1), (2,2,()), (2,2,1), (2,2,2).
a(3) = 34: (111,(),()), (111,1,()), (111,1,1), (111,11,()), (111,11,1), (111,11,11), (111,111,()), (111,111,1), (111,111,11), (111,111,111), (21,(),()), (21,1,()), (21,1,1), (21,11,()), (21,11,1), (21,11,11), (21,2,()), (21,2,1), (21,2,2), (21,21,()), (21,21,1), (21,21,11), (21,21,2), (21,21,21), (3,(),()), (3,1,()), (3,1,1), (3,2,()), (3,2,1), (3,2,2), (3,3,()), (3,3,1), (3,3,2), (3,3,3).

Crossrefs

Cf. A000041, A297388.

Sequence in context: A304975 A226546 A073372 * A026573 A326660 A225075

Adjacent sequences: A305020 A305021 A305022 * A305024 A305025 A305026

Keyword

nonn

Author

Alois P. Heinz, May 23 2018

Status

approved