A005575 a(n) = A259095(2n,n). (Formerly M1390)

0, 0, 1, 2, 5, 11, 20, 37, 63, 110, 174, 283, 435, 671, 1001, 1492, 2160, 3127, 4442, 6269, 8739, 12109, 16597, 22618, 30576, 41077, 54834, 72788, 96056, 126131, 164829, 214327, 277534, 357810, 459507, 587779, 749220, 951473, 1204501, 1519691, 1911618, 2397247, 2997985, 3738482, 4649981, 5768457, 7138640, 8812704, 10854735, 13339286

Offset

1,4

Comments

Computed by R. K. Guy in 1988.

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..900

F. C. Auluck, On some new types of partitions associated with generalized Ferrers graphs, Proc. Cambridge Philos. Soc. 47, (1951), 679-686.

R. K. Guy, Letter to N. J. A. Sloane, Apr 08 1988 (annotated scanned copy, included with permission)

E. M. Wright, Stacks, III, Quart. J. Math. Oxford, 23 (1972), 153-158.

Maple

b:= proc(n, i, d) option remember; `if`(i*(i+1)/2<n, 0,
     `if`(n=0, 1, b(n, i-1, d+1)+`if`(i>n, 0, d*b(n-i, i-1, 1))))
    end:
a:= n-> b(n, n-1, 1):
seq(a(n), n=1..50);  # Alois P. Heinz, Jul 08 2016

Mathematica

b[n_, i_, d_] := b[n, i, d] = If[i*(i+1)/2 < n, 0, If[n == 0, 1, b[n, i-1, d+1] + If[i > n, 0, d*b[n-i, i-1, 1]]]];
a[n_] := b[n, n-1, 1];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 28 2016, after Alois P. Heinz *)

Crossrefs

Cf. A259095, A005576, A005577.

Sequence in context: A022908 A256310 A026390 * A328670 A294745 A352234

Adjacent sequences: A005572 A005573 A005574 * A005576 A005577 A005578

Keyword

nonn,nice

Author

N. J. A. Sloane, R. K. Guy

Extensions

Edited by N. J. A. Sloane, Jun 20 2015

Terms a(25) and beyond from Joerg Arndt, Apr 09 2016

Status

approved