cp's OEIS Frontend

A089292 G.f.: Product_{m>=1} 1/(1-x^m)^A018819(m).

%I A089292 #12 Oct 02 2018 16:16:20
%S A089292 1,1,3,5,12,20,41,69,132,222,399,665,1156,1904,3212,5234,8645,13925,
%T A089292 22596,36008,57590,90862,143508,224316,350505,543159,840623,1292317,
%U A089292 1983094,3026178,4608061,6983663,10559800,15901698,23889722,35760786,53405395,79498207
%N A089292 G.f.: Product_{m>=1} 1/(1-x^m)^A018819(m).
%C A089292 Number of 2-dimensional partitions of n where each row is non-squashing.
%H A089292 Alois P. Heinz, <a href="/A089292/b089292.txt">Table of n, a(n) for n = 0..5000</a>
%H A089292 N. J. A. Sloane and J. A. Sellers, <a href="https://arxiv.org/abs/math/0312418">On non-squashing partitions</a>, arXiv:math/0312418 [math.CO], 2003.
%H A089292 N. J. A. Sloane and J. A. Sellers, <a href="https://doi.org/10.1016/j.disc.2004.11.014">On non-squashing partitions</a>, Discrete Math., 294 (2005), 259-274.
%e A089292 a(4) = 12:
%e A089292 4.31.3.22.2.211.21.2..2.11.11.1
%e A089292 .....1....2.....1..11.1.11.1..1
%e A089292 ......................1....1..1
%e A089292 ..............................1
%e A089292 211 and 1111 for example are excluded because they would squash.
%t A089292 maxm = 38;
%t A089292 b[0] = b[1] = 1; b[n_] := b[n] = If[OddQ[n], b[n-1], b[n-1] + b[n/2]];
%t A089292 Product[1/(1-x^m)^b[m], {m, 1, maxm}] + O[x]^maxm // CoefficientList[#, x]&
%t A089292 (* _Jean-François Alcover_, Oct 02 2018 *)
%Y A089292 Cf. A000123, A018819, A001970.
%K A089292 nonn
%O A089292 0,3
%A A089292 _N. J. A. Sloane_, Dec 24 2003