

A005577


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


4



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
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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

Joerg Arndt and 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) 679686.
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) 153158. MR0299575


MAPLE

b:= proc(n, i, d) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, b(n, i1, d+1)+`if`(i>n, 0, d*b(ni, i1, 1))))
end:
a:= n> max(seq(b(nr, r1, 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, i1, d+1] + If[i > n, 0, d*b[ni, i1, 1]]]];
a[n_] := Max[Table[b[nr, r1, 1], {r, 1, n}]];
Table[a[n], {n, 1, 60}] (* JeanFrançois 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



