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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. 3
1, 2, 8, 42, 264, 1920, 15840, 146160, 1491840, 16692480, 203212800, 2674425600, 37841126400, 572885913600, 9240898867200, 158228598528000, 2866422214656000, 54775863926784000, 1101208277385216000, 23234214178086912000, 513342323725271040000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..100

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.

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

MATHEMATICA

Table[(n - 2)! (n^2 - 3 n + 4) / 2, {n, 2, 30}] (* Vincenzo Librandi, Feb 10 2018 *)

PROG

(GAP) a:=List([2..23], n->(n^2-3*n+4)*Factorial(n-2)/2); # Muniru A Asiru, Feb 09 2018

(MAGMA) [Factorial(n-2)*(n^2-3*n+4)/2: n in [2..30]]; // Vincenzo Librandi, Feb 10 2018

CROSSREFS

Cf. A121634, A001710.

Sequence in context: A229285 A005315 A182520 * A002874 A078592 A225108

Adjacent sequences:  A121632 A121633 A121634 * A121636 A121637 A121638

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Aug 13 2006

STATUS

approved

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Last modified June 21 21:17 EDT 2018. Contains 305640 sequences. (Running on oeis4.)