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A356213
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Number of edge covers in the n-trapezohedral graph.
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1
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4, 104, 1699, 23904, 317044, 4101107, 52473796, 668177568, 8490113467, 107776172264, 1367566963756, 17349734444643, 220090218116188, 2791852592070632, 35414167120396459, 449219270600324928, 5698208011194600148, 72279907017666274643, 916846410588661477204
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OFFSET
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1,1
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COMMENTS
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Sequence extended to n = 1 using the formula/recurrence.
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LINKS
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FORMULA
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a(n) = 22*a(n-1) - 142*a(n-2) + 321*a(n-3) - 242*a(n-4) + 74*a(n-5) - 8*a(n-6) for n > 6.
G.f.: -(-2+x)*x*(2+9*x-6*x^2+2*x^3)/((1-3*x+x^2)*(1-6*x+2*x^2)*(1-13*x+4*x^2)).
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MATHEMATICA
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Table[LucasL[2 n] - 2 ((3 - Sqrt[7])^n + (3 + Sqrt[7])^n) + ((13 - 3 Sqrt[17])^n + (13 + 3 Sqrt[17])^n)/2^n, {n, 20}] // Expand (* Eric W. Weisstein, May 26 2024 *)
LinearRecurrence[{22, -142, 321, -242, 74, -8}, {4, 104, 1699, 23904, 317044, 4101107}, 20] (* Eric W. Weisstein, May 26 2024 *)
CoefficientList[Series[-(((-2 + x) (2 + 9 x - 6 x^2 + 2 x^3))/((1 - 3 x + x^2) (1 - 6 x + 2 x^2) (1 - 13 x + 4 x^2))), {x, 0, 20}], x] (* Eric W. Weisstein, May 26 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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