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Search: id:A100822
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| A100822 |
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Triangle read by rows: T(n,k) is the number of deco polyominoes of height n with k cells in the first column. (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
4
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| 1, 1, 1, 2, 3, 1, 6, 8, 9, 1, 24, 30, 32, 33, 1, 120, 144, 150, 152, 153, 1, 720, 840, 864, 870, 872, 873, 1, 5040, 5760, 5880, 5904, 5910, 5912, 5913, 1, 40320, 45360, 46080, 46200, 46224, 46230, 46232, 46233, 1, 362880, 403200, 408240, 408960, 409080, 409104, 409110, 409112, 409113, 1
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row n has n terms. Rows are circular permutations of the rows of A054115. Column 1 and row sums yield A000142 (the factorial numbers). Column 2 yields A059171.
T(n+1,n)=A007489(n).
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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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T(n, k)=sum((n-j)!, j=1..k) for 1<=k<n; T(n, n)=1.
T(n,k)=T(n-1,k-1)+(n-1)! for k<n; T(n,n)=1.
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EXAMPLE
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Triangle begins:
1;
1,1;
2,3,1;
6,8,9,1;
24,30,32,33,1;
T(2,1)=T(2,2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes, having, respectively, 1 and 2 cells in their first columns.
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MAPLE
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T:=proc(n, k) if k=n then 1 elif k<n then sum((n-j)!, j=1..k) else 0 fi end: for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000142, A054115, A059171, A007489.
Adjacent sequences: A100819 A100820 A100821 this_sequence A100823 A100824 A100825
Sequence in context: A036039 A092271 A054115 this_sequence A086211 A110189 A132372
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 06 2005, Aug 09 2006
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