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A005577 Maxima of the rows of the triangle A259095.

%I A005577 M0495 #41 Oct 29 2023 21:12:26
%S A005577 1,1,1,2,3,4,5,6,7,9,11,15,20,27,35,44,56,73,91,115,148,186,227,283,
%T A005577 358,435,538,671,813,1001,1233,1492,1815,2223,2673,3247,3933,4713,
%U A005577 5683,6850,8170,9785,11725,13948,16587,19783,23468,27710,32942,38956,45852,54133,63879,75000,87909,103471,121273,141629
%N A005577 Maxima of the rows of the triangle A259095.
%C A005577 Computed by _R. K. Guy_ in 1988.
%D A005577 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005577 Alois P. Heinz, <a href="/A005577/b005577.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Joerg Arndt)
%H A005577 F. C. Auluck, <a href="http://dx.doi.org/10.1017/S0305004100027134">On some new types of partitions associated with generalized ferrers graphs</a>, Math. Proc. Camb. Phil. Soc. 47 (1951) 679-686.
%H A005577 R. K. Guy, <a href="/A259095/a259095.pdf">Letter to N. J. A. Sloane, Apr 08 1988</a> (annotated scanned copy, included with permission)
%H A005577 E. M. Wright, <a href="http://dx.doi.org/10.1093/qmath/23.2.153">Stacks (III)</a>, The Quarterly J. of Math. (Oxford Journals), 23 (2) (1972) 153-158. <a href="http://www.ams.org/mathscinet-getitem?mr=299575">MR0299575</a>
%p A005577 b:= proc(n, i, d) option remember; `if`(i*(i+1)/2<n, 0,
%p A005577      `if`(n=0, 1, b(n, i-1, d+1)+`if`(i>n, 0, d*b(n-i, i-1, 1))))
%p A005577     end:
%p A005577 a:= n-> max(seq(b(n-r, r-1, 1), r=1..n)):
%p A005577 seq(a(n), n=1..60);  # _Alois P. Heinz_, Jul 08 2016
%t A005577 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]]]];
%t A005577 a[n_] := Max[Table[b[n-r, r-1, 1], {r, 1, n}]];
%t A005577 Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Jul 28 2016, after _Alois P. Heinz_ *)
%Y A005577 Cf. A259095, A005575, A005576.
%K A005577 nonn,nice
%O A005577 1,4
%A A005577 _N. J. A. Sloane_, _R. K. Guy_
%E A005577 Edited by _N. J. A. Sloane_, Jun 20 2015