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A192858
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Hosoya indices of the 2n-wheel graphs W_{2n}.
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1
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2, 10, 36, 120, 382, 1178, 3550, 10514, 30720, 88788, 254342, 723190, 2043386, 5742490, 16062492, 44744688, 124192270, 343594514, 947857750, 2608015778, 7159034232, 19609583820, 53608363286, 146290947310, 398552156402, 1084153113898, 2944982283540, 7989231439464, 21646950044830, 58585895022218, 158389325993422
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OFFSET
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1,1
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COMMENTS
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Wheel graphs are defined for n >= 4; extended to n=2 using recurrence.
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
G.f.: 2*x*(1+x)*(x-1)^2 / ( (x^2 - 3*x + 1)^2 ). - R. J. Mathar, Jul 11 2011
a(n) = ((3+r)^n*((5-r)*n+3*r-5) + (3-r)^n*((5+r)*n-3*r-5))/(5*2^n) with r=sqrt(5). - Bruno Berselli, Aug 31 2011
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MATHEMATICA
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LinearRecurrence[{6, -11, 6, -1}, {10, 36, 120, 382}, {0, 30}]
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PROG
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(Magma) I:=[2, 10, 36, 120]; [n le 4 select I[n] else 6*Self(n-1)-11*Self(n-2)+6*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Aug 31 2011
(PARI) x='x+O('x^30); Vec(2*x*(1+x)*(x-1)^2/((x^2-3*x+1)^2)) \\ G. C. Greubel, Nov 10 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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