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A030518
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Number of walks of length n between two vertices on an icosahedron at distance 2.
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4
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0, 2, 8, 52, 248, 1302, 6448, 32552, 162448, 813802, 4067448, 20345052, 101717448, 508626302, 2543092448, 12715657552, 63578092448, 317891438802, 1589456217448, 7947285970052, 39736424967448, 198682149251302, 993410721842448, 4967053731282552
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2*A030517(n-1) + 2*a(n-1) + 5*a(n-2).
a(n) = 5^n/12 - (-1)^n/12 - (sqrt(5))^(n+1)/20 - (-sqrt(5))^(n+1)/20.
a(n) = 4*a(n-1) + 10*a(n-2) - 20*a(n-3) - 25*a(n-4). (End)
G.f.: 2*x^2 / ((1 + x)*(1 - 5*x)*(1 - 5*x^2)).
a(n) = (5^n - 1)/12 for n even.
a(n) = (-6*5^((n-1)/2) + 5^n + 1)/12 for n odd. (End)
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PROG
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(PARI) concat(0, Vec(2*x^2/((1+x)*(1-5*x)*(1-5*x^2)) + O(x^30))) \\ Colin Barker, Oct 17 2016
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CROSSREFS
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KEYWORD
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nonn,walk,easy
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AUTHOR
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STATUS
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approved
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