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A121754 Number of columns ending at an even level in 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, 6, 31, 211, 1530, 13086, 120888, 1260792, 14140080, 174692880, 2304970560, 32969263680, 500368821120, 8139251433600, 139686867532800, 2547638477798400, 48786683184691200, 986263089841612800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n)=Sum(k*A121698(n,k),k=1..n-1).

REFERENCES

E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.

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

LINKS

Table of n, a(n) for n=1..19.

FORMULA

Recurrence relation: a(n)=(2n-3)a(n-1)-(n-1)(n-3)a(n-2)+(n-2)![n-2+(1/2)(1+(-1)^(n-1))(n-1)] for n>=3; a(1)=0, a(2)=1.

Conjecture D-finite with recurrence 16*(n+1)*a(n) +(-16*n^2-178*n+531)*a(n-1) +(-16*n^3+178*n^2-393*n-510)*a(n-2) +(16*n^4+98*n^3-1439*n^2+4222*n-3623)*a(n-3) +(-146*n^4+1479*n^3-4483*n^2+3054*n+2841)*a(n-4) +(130*n-311)*(n-6)*(-4+n)^2*a(n-5)=0. - R. J. Mathar, Jul 26 2022

EXAMPLE

a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 1 and 0 columns ending at an even level, respectively.

MAPLE

a[1]:=0: a[2]:=1: for n from 3 to 22 do a[n]:=(2*n-3)*a[n-1]-(n-1)*(n-3)*a[n-2]+(n-2)!*(n-2+(1/2)*(1+(-1)^(n-1))*(n-1)) od: seq(a[n], n=1..22);

CROSSREFS

Cf. A121698, A121752.

Sequence in context: A338674 A199320 A097176 * A351818 A200775 A244255

Adjacent sequences:  A121751 A121752 A121753 * A121755 A121756 A121757

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 23 2006

STATUS

approved

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Last modified October 2 08:07 EDT 2022. Contains 357191 sequences. (Running on oeis4.)