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

1, 1, 3, 5, 12, 20, 41, 69, 132, 222, 399, 665, 1156, 1904, 3212, 5234, 8645, 13925, 22596, 36008, 57590, 90862, 143508, 224316, 350505, 543159, 840623, 1292317, 1983094, 3026178, 4608061, 6983663, 10559800, 15901698, 23889722, 35760786, 53405395, 79498207

Offset: 0

Author

N. J. A. Sloane, Dec 24 2003

Keywords

• nonn

Comments

Number of 2-dimensional partitions of n where each row is non-squashing.

Examples

			a(4) = 12:
4.31.3.22.2.211.21.2..2.11.11.1
.....1....2.....1..11.1.11.1..1
......................1....1..1
..............................1
211 and 1111 for example are excluded because they would squash.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000
• N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, arXiv:math/0312418 [math.CO], 2003.
• N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

Crossrefs

Cf. A000123, A018819, A001970.

Programs

Mathematica

maxm = 38;
b[0] = b[1] = 1; b[n_] := b[n] = If[OddQ[n], b[n-1], b[n-1] + b[n/2]];
Product[1/(1-x^m)^b[m], {m, 1, maxm}] + O[x]^maxm // CoefficientList[#, x]&
(* Jean-François Alcover, Oct 02 2018 *)