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Search: id:A121750
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| A121750 |
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Number of columns of even 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. |
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+0
3
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| 0, 1, 5, 26, 184, 1338, 11652, 108210, 1140336, 12849714, 159858900, 2117522754, 30442090248, 463511103426, 7569181895436, 130254363597330, 2383020441932256, 45738553437874962, 927010880040945924
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A121748(n,k), k=0..n-1).
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REFERENCES
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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.
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FORMULA
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Recurrence relation: a(n)=n*a[n-1]+d(n-1)+(n-1)!*floor((n-1)/2) for n>=2, a(1)=0, where d(1)=1, d(2)=0, d(2n)=3!+5!+...+(2n-1)!, d(2n+1)=-d(2n).
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EXAMPLE
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a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 1 and 0 columns of even length, respectively.
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MAPLE
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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]:=0: for n from 2 to 22 do a[n]:=n*a[n-1]+d(n-1)+(n-1)!*floor((n-1)/2) od: seq(a[n], n=1..22);
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CROSSREFS
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Cf. A121747, A121748.
Adjacent sequences: A121747 A121748 A121749 this_sequence A121751 A121752 A121753
Sequence in context: A057793 A090226 A094422 this_sequence A143341 A007286 A099032
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 20 2006
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