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

Author

Alois P. Heinz, May 23 2018

Keywords

• nonn

Examples

			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).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Ferrers Diagram
• Wikipedia, Ferrers diagram

Crossrefs

Cf. A000041, A297388.