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A051928
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Number of independent sets of vertices in graph K_3 X C_n (n > 2).
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2
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4, 1, 13, 34, 121, 391, 1300, 4285, 14161, 46762, 154453, 510115, 1684804, 5564521, 18378373, 60699634, 200477281, 662131471, 2186871700, 7222746565, 23855111401, 78788080762, 260219353693, 859446141835, 2838557779204, 9375119479441, 30963916217533
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 4*a(n-2) + a(n-3).
G.f.: (4-7*x-5*x^2)/((1+x)*(1-3*x-x^2)). - Colin Barker, May 22 2012
a(n) = 2*(-1)^n + ((3-sqrt(13))/2)^n + ((3+sqrt(13))/2)^n. - Colin Barker, May 11 2017
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MATHEMATICA
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LinearRecurrence[{2, 4, 1}, {4, 1, 13}, 30] (* Harvey P. Dale, Nov 20 2021 *)
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PROG
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(PARI) Vec((4-7*x-5*x^2)/((1+x)*(1-3*x-x^2)) + O(x^30)) \\ Colin Barker, May 11 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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