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Search: id:A091147
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| A091147 |
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Expansion of (1-x-sqrt(1-2x-15x^2))/(8x^2). |
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+0
1
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| 1, 1, 5, 13, 57, 201, 861, 3445, 14897, 63313, 278389, 1223069, 5465065, 24513945, 111037005, 505298565, 2314343265, 10645982625, 49202944485, 228253816365, 1062783893145, 4964167491945, 23256852644925, 109249893866133
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=A014433(n+1)/4
Number of lattice paths in the first quadrant from (0,0) to (n,0) using only steps H=(1,0), U=(1,1) and D=(1,-1), where the U steps come in 4 colors (i.e. Motzkin paths with the up steps in 4 colors). Series reversion of x/(1+x+4x^2). - Paul Barry (pbarry(AT)wit.ie), May 16 2005
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FORMULA
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G.f.: 2/(1-x+sqrt(1-2x-15x^2)); a(n)=sum{k=0..n, binomial(n, k)4^(k/2)C(k/2)(1+(-1)^k)/2}, C(n)=A000108(n).
a(n)=sum{k=0..n, C(n, 2k)C(k)4^k}; - Paul Barry (pbarry(AT)wit.ie), May 16 2005
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CROSSREFS
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Sequence in context: A149551 A149552 A084136 this_sequence A149553 A149554 A149555
Adjacent sequences: A091144 A091145 A091146 this_sequence A091148 A091149 A091150
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Dec 22 2003
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