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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
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
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 30 2007
STATUS
approved