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A121747 Number of columns of odd length 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
1, 2, 8, 44, 262, 1938, 15600, 145086, 1461888, 16438446, 198598860, 2623055166, 36933441912, 560697617214, 9014444990964, 154698782105070, 2795947673216544, 53529558912435438, 1074325981318055676 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)=Sum(k*A121745(n,k), k=0..n).

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)=n*a[n-1]-d(n-1)+(n-1)!*floor(n/2) for n>=2, a(1)=1, where d(1)=1, d(2)=0, d(2n)=3!+5!+...+(2n-1)!, d(2n+1)=-d(2n).

EXAMPLE

a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 0 and 2 columns of odd length, respectively.

MAPLE

d:=proc(n) if n=1 then 1 elif n=2 then 0 elif n mod 2 = 0 then add((2*j-1)!, j=2..n/2) else -d(n-1) fi end: a[1]:=1: for n from 2 to 22 do a[n]:=n*a[n-1]-d(n-1)+(n-1)!*floor(n/2) od: seq(a[n], n=1..22);

CROSSREFS

Cf. A121745, A121750.

Sequence in context: A291697 A047851 A177260 * A261266 A014508 A141147

Adjacent sequences:  A121744 A121745 A121746 * A121748 A121749 A121750

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 20 2006

STATUS

approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)