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A121746 Number of deco polyominoes of height n, consisting only of columns of even length. 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, 1, 3, 9, 27, 117, 459, 2421, 11979, 74421, 443979, 3184821, 22216779, 180996021, 1444706379, 13186615221, 118495279179, 1198323664821, 11969865775179, 132880218064821, 1460470704175179, 17659740362704821 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n)=A121745(n,0).

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..23.

FORMULA

Recurrence relation: a(n)=floor((n-1)/2)*a(n-1)+floor((n+1)/2)*a(n-2); a(1)=0, a(2)=1.

G.f.: Q(0)/(x*(1+x)) - 1/x, where Q(k)= 1 + x*(k+1)/(1 - x*(k+1)/(x*(k+1) + 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 23 2013

Let S=Sum_{n>=0} (1 + x*n + x)*x^(2*n)*(n!)^2, then g.f. A(x)=S/(x+x^2) - 1/x. - Sergei N. Gladkovskii, May 23 2013

EXAMPLE

a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes and only the vertical one consists only of columns of even length.

MAPLE

a[1]:=0: a[2]:=1: for n from 3 to 26 do a[n]:=floor((n-1)/2)*a[n-1]+floor((n+1)/2)*a[n-2] od: seq(a[n], n=1..26);

CROSSREFS

Cf. A121745, A121749.

Sequence in context: A148929 A148930 A230951 * A323927 A146151 A306681

Adjacent sequences:  A121743 A121744 A121745 * A121747 A121748 A121749

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 20 2006

STATUS

approved

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Last modified May 13 12:16 EDT 2021. Contains 343839 sequences. (Running on oeis4.)