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Search: id:A091149
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| A091149 |
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Expansion of (1-x-sqrt(1-2x-23x^2))/(12x^2). |
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+0
1
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| 1, 1, 7, 19, 109, 421, 2251, 10207, 53593, 263305, 1385263, 7109323, 37728901, 198723565, 1065245299, 5706564247, 30879236017, 167409942289, 913397457367, 4996676997379, 27455383898269, 151263170713909, 836158046041243
(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)=A014435(n+1)/6
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 6 colors (i.e. Motzkin paths with the up steps in 6 colors), or where the U steps come in 2 colors and the D steps in 3 (or vice versa). Series reversion of x/(1+x+6x^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-23x^2)); a(n)=sum{k=0..n, binomial(n, k)6^(k/2)C(k/2)(1+(-1)^k)/2}, C(n)=A000108(n).
a(n)=sum{k=0..n, C(n, 2k)C(k)6^k}; - Paul Barry (pbarry(AT)wit.ie), May 16 2005
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CROSSREFS
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Sequence in context: A084603 A088883 A026574 this_sequence A070976 A096321 A128338
Adjacent sequences: A091146 A091147 A091148 this_sequence A091150 A091151 A091152
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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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