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Search: id:A121298
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| A121298 |
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Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n and height k (1<=k<=n; here by the height of a polyomino one means the number of lines of slope -1 that pass through the centers of the polyomino cells). |
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+0
2
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| 1, 0, 2, 0, 1, 4, 0, 0, 5, 8, 0, 0, 3, 15, 16, 0, 0, 1, 17, 39, 32, 0, 0, 0, 15, 59, 95, 64, 0, 0, 0, 9, 75, 175, 223, 128, 0, 0, 0, 4, 78, 269, 479, 511, 256, 0, 0, 0, 1, 67, 358, 845, 1247, 1151, 512, 0, 0, 0, 0, 48, 419, 1300, 2461, 3135, 2559, 1024, 0, 0, 0, 0, 29, 432, 1801
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are the odd-subscripted Fibonacci numbers (A001519). Sum of terms in column k = A007808(k). Sum(k*T(n,k),k=0..n)=A121299(n).
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REFERENCES
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E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, La hauteur des polyominos dirige's verticalement convexes, Seminaire Lotharingien de Combinatoire, B31d (1993) [Formerly: Publ. I.R.M.A. Strasbourg, 1994/021, p. 5-15.]
E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
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LINKS
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E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, La hauteur des polyominos...
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FORMULA
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T(n,k)=T(n-1,k-1)+Sum(T(n-k,j), j=1..k-1)+Sum(T(n-j,k-1), j=1..k-1).
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EXAMPLE
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T(2,2)=2 because we have the vertical and the horizontal dominoes.
Triangle starts:
1;
0,2;
0,1,4;
0,0,5,8;
0,0,3,15,16;
0,0,1,17,39,32;
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MAPLE
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T:=proc(n, k) if n<=0 or k<=0 then 0 elif n=1 and k=1 then 1 else T(n-1, k-1)+add(T(n-k, j), j=1..k-1)+add(T(n-j, k-1), j=1..k-1) fi end: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001519, A007808, A121299.
Sequence in context: A061290 A099096 A099089 this_sequence A121462 A131487 A039991
Adjacent sequences: A121295 A121296 A121297 this_sequence A121299 A121300 A121301
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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), Aug 04 2006
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