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Search: id:A066822
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| A066822 |
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The fourth row of A038622, triangular array that counts rooted polyominoes. |
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+0
1
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| 1, 5, 20, 71, 238, 770, 2436, 7590, 23397, 71566, 217646, 659022, 1988805, 5986176, 17980968, 53922096, 161492571, 483149385, 1444245936, 4314214443, 12880107548
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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There is a general solution for all rows of this triangular array: For the k-th row and n-th term on this row: a(0)=0; a(1)=1; a(n) = (2*k-1+n)*n*a(n) = 2*(n+k)*(n+k-1)*a(n-1) + 3*(n+k-1)*(n+k-2)*a(n-2)
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REFERENCES
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D. Gouyou-Beauchamps and G. Viennot, Equivalence of the two-dimensional directed animal problem to a one-dimensional path problem, Adv. in Appl. Math. 9 (1988), no. 3, 334-357.
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FORMULA
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a(0)=0; a(1)=1; (n+7)*n*a(n)=2*(n+4)*(n+3)*a(n-1) + 3*(n+3)*(n+2)*a(n-2)
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PROGRAM
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(PARI) s=[0, 1]; {A038622(n, k)=if(n==0, 1, t=(2*(n+k)*(n+k-1)*s[2]+3*(n+k-1)*(n+k-2)*s[1])/((n+2*k-1)*n); s[1]=s[2]; s[2]=t; t)}
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CROSSREFS
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Cf. A038622.
Sequence in context: A054444 A121332 A122695 this_sequence A137212 A118049 A114247
Adjacent sequences: A066819 A066820 A066821 this_sequence A066823 A066824 A066825
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Randall L. Rathbun, Jan 19 2002
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