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
Examples
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.
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.
Programs
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Maple
a:= n-> `if`(n=1, 1, (n^2-3*n+4)*(n-2)!/2): seq(a(n), n=1..23);
Formula
a(n) = A121634(n,0).
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
Extensions
Missing a(1) inserted by Alois P. Heinz, Nov 25 2018