A005577 Maxima of the rows of the triangle A259095.

1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 20, 27, 35, 44, 56, 73, 91, 115, 148, 186, 227, 283, 358, 435, 538, 671, 813, 1001, 1233, 1492, 1815, 2223, 2673, 3247, 3933, 4713, 5683, 6850, 8170, 9785, 11725, 13948, 16587, 19783, 23468, 27710, 32942, 38956, 45852, 54133, 63879, 75000, 87909, 103471, 121273, 141629

Offset: 1

Author

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

Keywords

• nonn
• nice

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..1000 (first 100 terms from Joerg Arndt)
• F. C. Auluck, On some new types of partitions associated with generalized ferrers graphs, Math. Proc. Camb. Phil. 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), The Quarterly J. of Math. (Oxford Journals), 23 (2) (1972) 153-158. MR0299575

Crossrefs

Cf. A259095, A005575, A005576.

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-> max(seq(b(n-r, r-1, 1), r=1..n)):
seq(a(n), n=1..60);  # 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_] := Max[Table[b[n-r, r-1, 1], {r, 1, n}]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jul 28 2016, after Alois P. Heinz *)

Extensions

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