

A134437


Number of cells in the 2nd rows of all deco polyominoes of height n. A deco polyomino is a directed columnconvex 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
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OFFSET

1,3


COMMENTS

a(n) = Sum_{k=0..n1} k*A134436(n,k).


REFERENCES

E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.


LINKS

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


FORMULA

a(n) = (1/4)*(3n2)*(n1)*(n1)!.
a(n) = (1/2)*(3n4)*(n1)! + (n1)*a(n1); a(1)=0.
a(n) = (n+2)!*Sum_{k=1..n} ((2*k1)/(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*n2)*(n1)*factorial(n1), n = 1 .. 18)


MATHEMATICA

Table[((3n2)(n1)(n1)!)/4, {n, 20}] (* Harvey P. Dale, Sep 23 2011 *)


PROG

(MAGMA)[(3*n2)*(n1)*Factorial(n1)/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



