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

0,4

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

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

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

Crossrefs

Essentially the same as A048574.

Cf. A000712, A304789.

Sequence in context: A034357 A023626 A048574 * A052821 A292445 A023628

Adjacent sequences: A052834 A052835 A052836 * A052838 A052839 A052840

Keyword

easy,nonn

Author

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

Extensions

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

New name from Alois P. Heinz, May 26 2018

Status

approved