A121635 Number of deco polyominoes of height n, having no 2-cell columns starting at level 0. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

1, 1, 2, 8, 42, 264, 1920, 15840, 146160, 1491840, 16692480, 203212800, 2674425600, 37841126400, 572885913600, 9240898867200, 158228598528000, 2866422214656000, 54775863926784000, 1101208277385216000, 23234214178086912000, 513342323725271040000

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..450 (n=2..101 from Muniru A Asiru)

E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.

Mark Dukes, Chris D White, Web Matrices: Structural Properties and Generating Combinatorial Identities, arXiv:1603.01589 [math.CO], 2016.

Mark Dukes, Chris D. White, Web Matrices: Structural Properties and Generating Combinatorial Identities, Electronic Journal Of Combinatorics, 23(1) (2016), #P1.45.

Formula

a(n) = A121634(n,0).

a(1)=1, a(n) = (n-2)!(n^2-3*n+4)/2 = A000142(n-2)*A152947(n) for n>=2.

a(1)=1, a(2)=1, a(n) = (n-2)*[(n-2)! + a(n-1)] for n>=3.

D-finite with recurrence a(n) +(-n-2)*a(n-1) +2*(n-1)*a(n-2) +2*(-n+4)*a(n-3)=0. - R. J. Mathar, Jul 26 2022

Example

a(2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes and the horizontal one has no 2-cell column starting at level 0.

Maple

a:= n-> `if`(n=1, 1, (n^2-3*n+4)*(n-2)!/2): seq(a(n), n=1..23);

Crossrefs

Cf. A121634, A001710.

Sequence in context: A339460 A005315 A182520 * A002874 A324961 A351814

Adjacent sequences: A121632 A121633 A121634 * A121636 A121637 A121638

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 13 2006

Extensions

Missing a(1) inserted by Alois P. Heinz, Nov 25 2018

Status

approved