A301772 Number of odd chordless cycles in the n-antiprism graph.

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

Table of n, a(n) for n=0..37.

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)/( (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 A029593

Adjacent sequences: A301769 A301770 A301771 * A301773 A301774 A301775

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 26 2018

Status

approved