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Search: id:A101491
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| A101491 |
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Triangle T(n,k), read by rows: number of Kn{\"o}del walks starting at 0, ending at k, with n steps. |
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+0
2
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| 1, 0, 1, 2, 1, 1, 1, 3, 1, 1, 5, 4, 4, 1, 1, 5, 10, 5, 5, 1, 1, 15, 15, 15, 6, 6, 1, 1, 20, 35, 21, 21, 7, 7, 1, 1, 50, 56, 56, 28, 28, 8, 8, 1, 1, 76, 126, 84, 84, 36, 36, 9, 9, 1, 1, 176, 210, 210, 120, 120, 45, 45, 10, 10, 1, 1, 286, 462, 330, 330, 165, 165, 55, 55, 11, 11, 1, 1
(list; table; graph; listen)
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OFFSET
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0,4
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LINKS
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H. Prodinger, The Kernel Method: a collection of examples
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FORMULA
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G.f.: r(z)/[z(1+z)(1-r(z))]*(1+xzr(z))/(1-xr(z)), with r(z)=(1-sqrt(1-4z^2)/2z. Then the g.f. of the k-th column is r(z)^(k+1)/[z(1-r(z))].
T(n, k) = Sum{i=0..n, (-1)^(n-i)*C(i, [i/2]) } for k=0, otherwise T(n, k) = C(n, [(n-k)/2]).
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EXAMPLE
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1,
0,1,
2,1,1,
1,3,1,1,
5,4,4,1,1,
5,10,5,5,1,1,
15,15,15,6,6,1,1,
20,35,21,21,7,7,1,1,
50,56,56,28,28,8,8,1,1,
76,126,84,84,36,36,9,9,1,1,
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CROSSREFS
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Left-hand columns include A086905, A037952, A037955, A037951, A037956, A037953, A037957, A037954, A037958.
Sequence in context: A047150 A102054 A111604 this_sequence A032436 A073408 A120454
Adjacent sequences: A101488 A101489 A101490 this_sequence A101492 A101493 A101494
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Jan 21 2005
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