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A121580
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Number of cells in column 1 of 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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2
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1, 3, 11, 53, 317, 2237, 18077, 164237, 1656077, 18348557, 221561357, 2895986957, 40737113357, 613623026957, 9854521894157, 168083120422157, 3034505335078157, 57810369261862157, 1159018646647078157
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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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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LINKS
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FORMULA
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a(1)=1, a(n)=a(n-1)+(n-1)!*([1+n(n-1)/2] for n>=2.
Conjecture D-finite with recurrence a(n) +(-n-4)*a(n-1) +3*(n+1)*a(n-2) +2*(-2*n+3)*a(n-3) +2*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 26 2022
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EXAMPLE
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a(2)=3 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 2 and 1 cells in their first columns.
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MAPLE
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a[1]:=1: for n from 2 to 22 do a[n]:=a[n-1]+(n-1)!*(1+n*(n-1)/2) od: seq(a[n], n=1..22);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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