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Search: id:A078789
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| A078789 |
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Expansion of (1-4x+2x^2)/(1-7x+13x^2-4x^3). |
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+0
2
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| 1, 3, 10, 35, 127, 474, 1807, 6995, 27370, 107883, 427351, 1698458, 6765175, 26985675, 107746282, 430470899, 1720537327, 6878624730, 27505271455, 109996928003, 439924466026, 1759532283963, 7037695641415, 28149647662490
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of walks of length 2n+1 between two adjacent vertices in the cycle graph C_10. - Herbert Kociemba (kociemba(AT)t-online.de), Jul 02 2004
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FORMULA
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G.f.: (1-4x+2x^2)/(1-7x+13x^2-4x^3).
a(5n+3)=A049016(10n+3), a(5n+4)=A049016(10n+5).
Let phi be the golden ratio (1+Sqrt(5))/2. Then a(n) = [4^(n+1) + (Sqrt(5)+3)phi^(2n) - (Sqrt(5)-3)phi^(-2n)]/10 a(n)=7a(n-1)-13a(n-2)+4a(n-3). - Herbert Kociemba (kociemba(AT)t-online.de), Jul 02 2004
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PROGRAM
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(PARI) a(n)=polcoeff((1-4*x+2*x^2)/(1-7*x+13*x^2-4*x^3)+x*O(x^n), n)
(PARI) a(n)=sum(k=-n\5, n\5, binomial(2*n+1, n+1+5*k))
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CROSSREFS
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Cf. A049016.
Sequence in context: A149036 A047127 A114196 this_sequence A128736 A149037 A151046
Adjacent sequences: A078786 A078787 A078788 this_sequence A078790 A078791 A078792
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Dec 03, 2002
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