A005577 Maxima of the rows of the triangle A259095. (Formerly M0495)

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

1,4

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..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

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-> 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 *)

Crossrefs

Cf. A259095, A005575, A005576.

Sequence in context: A131617 A214321 A320318 * A263362 A336733 A072966

Adjacent sequences: A005574 A005575 A005576 * A005578 A005579 A005580

Keyword

nonn,nice

Author

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

Extensions

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

Status

approved