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A294152
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Chromatic invariant of the n-antiprism graph.
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2
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0, 2, 11, 38, 112, 309, 828, 2190, 5759, 15106, 39580, 103657, 271416, 710618, 1860467, 4870814, 12752008, 33385245, 87403764, 228826086, 599074535, 1568397562, 4106118196, 10749957073, 28143753072, 73681302194, 192900153563, 505019158550, 1322157322144
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OFFSET
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1,2
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COMMENTS
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Extended to a(1)-a(2) using the formula/recurrence.
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LINKS
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FORMULA
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a(n) = phi^(2*n) + phi^(-2*n) - 2*n - 1.
a(n) = 5*a(n-1) - 8*a(n-2) + 5*a(n-3) - a(n-4).
G.f.: x^2*(2 + x - x^2)/((-1 + x)^2*(1 - 3*x + x^2)).
a(n) = -1 + ((3-sqrt(5))/2)^n + ((3+sqrt(5))/2)^n - 2*n. - Colin Barker, Nov 16 2017
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MATHEMATICA
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Table[LucasL[2 n] - 2 n - 1, {n, 3, 20}]
LinearRecurrence[{5, -8, 5, -1}, {0, 2, 11, 38}, 20]
CoefficientList[Series[(x (2 + x - x^2))/((-1 + x)^2 (1 - 3 x + x^2)), {x, 0, 20}], x]
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PROG
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(PARI) concat(0, Vec(x^2*(2 + x - x^2)/((-1 + x)^2*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Nov 16 2017
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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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