A005576 The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r. (Formerly M0583)

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

0,3

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.

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)/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 *)

Crossrefs

Cf. A259095, A005575, A005577.

Sequence in context: A191015 A181385 A188381 * A339592 A241131 A339397

Adjacent sequences: A005573 A005574 A005575 * A005577 A005578 A005579

Keyword

nonn,nice

Author

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

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

Status

approved