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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. 2
0, 1, 7, 45, 312, 2400, 20520, 194040, 2016000, 22861440, 281232000, 3732220800, 53169177600, 809512704000, 13120332825600, 225573828480000, 4100866818048000, 78606921609216000 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified December 2 23:09 EST 2020. Contains 338898 sequences. (Running on oeis4.)