A052837 Number of partitions of 2n whose Ferrers-Young diagram allows more than one different domino tiling.

0, 0, 1, 4, 10, 22, 43, 80, 141, 240, 397, 640, 1011, 1568, 2395, 3604, 5360, 7876, 11460, 16510, 23588, 33418, 47006, 65640, 91085, 125596, 172215, 234820, 318579, 430060, 577920, 773130, 1030007, 1366644, 1806445, 2378892, 3121835, 4082796, 5322360, 6916360

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

The original name was: A simple grammar.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 804

Crossrefs

Essentially the same as A048574.

Cf. A000712, A304789.

Programs

Maple

spec := [S,{C=Sequence(Z,1 <= card),B=Set(C,1 <= card),S=Prod(B,B)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
# second Maple program:
a:= n-> (p-> add(p(j)*p(n-j), j=1..n-1))(combinat[numbpart]):
seq(a(n), n=0..40);  # Alois P. Heinz, May 26 2018

Mathematica

a[n_] := If[n <= 1, 0, With[{pp = Array[PartitionsP, n-1]},
   First[ListConvolve[pp, pp]]]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jan 30 2025 *)

Formula

G.f.: (exp(Sum_{j>=1} -x^j/((x^j-1)*j) )-1)^2.

a(n) = Sum_{k>=2} A304789(n,k). - Alois P. Heinz, May 26 2018

Extensions

More terms from Franklin T. Adams-Watters, Feb 08 2006

New name from Alois P. Heinz, May 26 2018