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Search: id:A121633
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| A121633 |
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Sum of the bottom levels of the last column over 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, 0, 1, 9, 68, 527, 4408, 40303, 403046, 4393339, 51955528, 663383135, 9102982354, 133668773755, 2092209897524, 34783032728383, 612234346270510, 11375905660965179, 222544581264066400, 4572536725690159999
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OFFSET
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1,4
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COMMENT
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a(n)=Sum(k*A121632(n,k),k>=0).
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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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FORMULA
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a(1)=0; a(n)=na(n-1)+(n-1)!-1 for n>=2.
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EXAMPLE
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a(2)=0 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, all of whose columns start at level 0.
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MAPLE
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a[1]:=0: for n from 2 to 23 do a[n]:=n*a[n-1]+(n-1)!-1 od: seq(a[n], n=1..23);
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CROSSREFS
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Cf. A121632, A000254.
Sequence in context: A002051 A133120 A048742 this_sequence A091708 A024119 A120306
Adjacent sequences: A121630 A121631 A121632 this_sequence A121634 A121635 A121636
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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 12 2006
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