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A121753 Number of deco polyominoes of height n in which all columns end at an odd level. 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, 1, 2, 6, 16, 62, 230, 1114, 5268, 30702, 176226, 1201638, 8107464, 63339702, 491010102, 4324845834, 37867131900, 371275954758, 3623124865986, 39137296073094, 421150512316032, 4969568447400366, 58455531552960198 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n)=A121698(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)=(1+2floor((n-2)/2))a(n-1)-[floor((n-1)/2)floor((n-2)/2)-1]a(n-2) for n>=3, a(1)=1, a(2)=1.

EXAMPLE

a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes and only the horizontal one has all of its columns ending at an odd level.

MAPLE

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

CROSSREFS

Cf. A121698, A121751.

Sequence in context: A093113 A150030 A150031 * A173994 A150032 A283420

Adjacent sequences:  A121750 A121751 A121752 * A121754 A121755 A121756

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 23 2006

STATUS

approved

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Last modified December 6 18:16 EST 2021. Contains 349567 sequences. (Running on oeis4.)