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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
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
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)/( (x^3-x^2-2*x-1)*(x^3-x^2+2*x-1)).
2*a(n) = -3*A077990(n) -4*A077990(n-1)-A077990(n-2) +3*A005314(n+1) -4*A005314(n)+A005314(n-1). - R. J. Mathar, Feb 25 2024
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: A350601 A293783 A274541 * A021497 A201735 A370832
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 26 2018
STATUS
approved