

A121749


Number of deco polyominoes of height n, consisting only of columns of odd length. A deco polyomino is a directed columnconvex polyomino in which the height, measured along the diagonal, is attained only in the last column.


2



1, 1, 2, 6, 16, 66, 246, 1248, 5976, 36120, 210480, 1479600, 10140480, 81340560, 640367280, 5773662720, 51312240000, 513773124480, 5085768280320, 55995414048000, 610811823283200, 7334879610643200, 87402605773190400
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OFFSET

1,3


COMMENTS



REFERENCES

E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 114.
E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.


LINKS



FORMULA

Recurrence relation: a(n)=floor(n/2)(a(n1)+a(n2)) for n>=3, a(1)=a(2)=1.
Dfinite with recurrence +4*a(n) 2*a(n1) +(n^2n+4)*a(n2) +2*(n+2)*a(n3) +(n2)*(n3)*a(n4)=0.  R. J. Mathar, Jul 26 2022


EXAMPLE

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


MAPLE

a[1]:=1: a[2]:=1: for n from 3 to 26 do a[n]:=floor(n/2)*(a[n1]+a[n2]) od: seq(a[n], n=1..26);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



