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 A301772 Number of odd chordless cycles in the n-antiprism graph. 0
 0, 2, 0, 2, 8, 2, 24, 16, 48, 92, 100, 310, 344, 808, 1344, 2102, 4480, 6462, 13092, 21662, 37488, 69904, 113652, 212844, 359856, 636402, 1134068, 1937072, 3493120, 6012746, 10639264, 18706394, 32550976, 57727738, 100407848, 177116816, 310493720, 543717148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence extended to a(0)-a(3) using the formula/recurrence (actual 3-antiprism count is 0). LINKS Eric Weisstein's World of Mathematics, Antiprism Graph Eric Weisstein's World of Mathematics, Chordless Cycle Index entries for linear recurrences with constant coefficients, signature (0, 2, 2, -1, 2, -1). FORMULA a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6). G.f.: 2*x*(1 - x^2 + 2*x^3)/(1 - 2*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6). MATHEMATICA Table[(RootSum[-1 + #1 - 2 #1^2 + #1^3 &, #1^n &] - RootSum[-1 + #1 + 2 #1^2 + #1^3 &, #1^n &])/2, {n, 0, 20}] LinearRecurrence[{0, 2, 2, -1, 2, -1}, {0, 2, 0, 2, 8, 2}, 20] CoefficientList[Series[2 x (1 - x^2 + 2 x^3)/(1 - 2 x^2 - 2 x^3 + x^4 - 2 x^5 + x^6), {x, 0, 20}], x] CROSSREFS Sequence in context: A211888 A293783 A274541 * A021497 A201735 A029593 Adjacent sequences:  A301769 A301770 A301771 * A301773 A301774 A301775 KEYWORD nonn AUTHOR Eric W. Weisstein, Mar 26 2018 STATUS approved

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Last modified September 18 06:42 EDT 2021. Contains 347510 sequences. (Running on oeis4.)