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A121634
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Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and having k 2-cell columns starting at level 0 (n>=1; 0<=k<=n-1). 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, 1, 1, 2, 3, 1, 8, 10, 5, 1, 42, 44, 25, 8, 1, 264, 242, 144, 57, 12, 1, 1920, 1594, 962, 429, 117, 17, 1, 15840, 12204, 7366, 3536, 1131, 219, 23, 1, 146160, 106308, 63766, 32118, 11453, 2664, 380, 30, 1, 1491840, 1036944, 616436, 320710, 123742, 32765
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums are the factorials (A000142). T(n,0)=A121635(n). Sum(k*T(n,k), k=0..n-1)=A121636(n)
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REFERENCES
| 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
| The row generating polynomials satisfy P(n,t)=(t+n-2)[(n-2)!+P(n-1,t)] for n>=3, P(1,t)=1 and P(2,t)=1+t.
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EXAMPLE
| T(2,0)=1 and T(2,1)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes, having, respectively, 0 and 1 columns with exactly 2 cells starting at level 0.
Triangle starts:
1;
1,1;
2,3,1;
8,10,5,1;
42,44,25,8,1;
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MAPLE
| P[1]:=1: P[2]:=1+t: for n from 3 to 11 do P[n]:=sort(expand((t+n-2)*((n-2)!+P[n-1]))) od: for n from 1 to 11 do seq(coeff(P[n], t, j), j=0..n-1) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A000142, A121635, A121636, A121585.
Sequence in context: A096063 A101281 A106033 * A006015 A110292 A138672
Adjacent sequences: A121631 A121632 A121633 * A121635 A121636 A121637
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 13 2006
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