A134437 Number of cells in the 2nd rows of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

0, 1, 7, 45, 312, 2400, 20520, 194040, 2016000, 22861440, 281232000, 3732220800, 53169177600, 809512704000, 13120332825600, 225573828480000, 4100866818048000, 78606921609216000

Offset

1,3

Comments

a(n) = Sum_{k=0..n-1} k*A134436(n,k).

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..400

Formula

a(n) = (1/4)*(3n-2)*(n-1)*(n-1)!.

a(n) = (1/2)*(3n-4)*(n-1)! + (n-1)*a(n-1); a(1)=0.

a(n) = (n+2)!*Sum_{k=1..n} ((2*k-1)/(k*(k+1)*(k+2))). - Gary Detlefs, Sep 20 2011

D-finite with recurrence +3*a(n) +(-3*n-11)*a(n-1) +2*(4*n-3)*a(n-2) +2*(-n+3)*a(n-3)=0. - R. J. Mathar, Jul 26 2022

Example

a(2)=1 because the horizontal domino has no cells in the 2nd row and the vertical domino has 1 cell in the 2nd row.

Maple

seq((1/4)*(3*n-2)*(n-1)*factorial(n-1), n = 1 .. 18)

Mathematica

Table[((3n-2)(n-1)(n-1)!)/4, {n, 20}] (* Harvey P. Dale, Sep 23 2011 *)

Prog

(Magma)[(3*n-2)*(n-1)*Factorial(n-1)/4: n in [1..20]]; // Vincenzo Librandi, Sep 24 2011

Crossrefs

Cf. A134436.

Sequence in context: A301319 A143835 A103719 * A018927 A001266 A071971

Adjacent sequences: A134434 A134435 A134436 * A134438 A134439 A134440

Keyword

nonn

Author

Emeric Deutsch, Nov 30 2007

Status

approved