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 A121749 Number of deco polyominoes of height n, consisting only of columns of odd 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
 1, 1, 2, 6, 16, 66, 246, 1248, 5976, 36120, 210480, 1479600, 10140480, 81340560, 640367280, 5773662720, 51312240000, 513773124480, 5085768280320, 55995414048000, 610811823283200, 7334879610643200, 87402605773190400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n)=A121748(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/2)(a(n-1)+a(n-2)) for n>=3, a(1)=a(2)=1. D-finite with recurrence +4*a(n) -2*a(n-1) +(-n^2-n+4)*a(n-2) +2*(-n+2)*a(n-3) +(n-2)*(n-3)*a(n-4)=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[n-1]+a[n-2]) od: seq(a[n], n=1..26); CROSSREFS Cf. A121746, A121748. Sequence in context: A363587 A150032 A283420 * A009386 A009605 A009681 Adjacent sequences: A121746 A121747 A121748 * A121750 A121751 A121752 KEYWORD nonn AUTHOR Emeric Deutsch, Aug 20 2006 STATUS approved

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Last modified May 26 11:45 EDT 2024. Contains 372824 sequences. (Running on oeis4.)