A005576 The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r.

1, 1, 2, 3, 4, 7, 9, 13, 17, 25, 32, 43, 56, 73, 95, 122, 155, 196, 248, 309, 388, 480, 595, 731, 899, 1096, 1338, 1624, 1967, 2373, 2860, 3431, 4111, 4911, 5853, 6963, 8263, 9785, 11565, 13646, 16064, 18884, 22155, 25953, 30349, 35441, 41311, 48098, 55906, 64900, 75231, 87103, 100702, 116296, 134130, 154522

Offset: 0

Author

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

Keywords

• nonn
• nice

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 = 0..5000 (first 143 terms from Joerg Arndt)
• Joerg Arndt, C++ program to compute this sequence, 2016
• 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.

Crossrefs

Cf. A259095, A005575, A005577.

Programs

Maple

b:= proc(n, i, d) option remember; `if`(i*(i+1)/2n, 0, d*b(n-i, i-1, 1))))
    end:
a:= n-> b(n*(n-1)/2, n, 1):
seq(a(n), n=0..55);  # 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)/2, n, 1];
Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jul 28 2016, after Alois P. Heinz *)

Extensions

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

Terms a(0)..a(11) computed by R. K. Guy

Terms a(12)=56 and beyond from Joerg Arndt, Apr 10 2016