A301774 Number of odd chordless cycles in the (2n+1)-prism graph.

2, 12, 30, 74, 200, 522, 1362, 3572, 9350, 24474, 64080, 167762, 439202, 1149852, 3010350, 7881194, 20633240, 54018522, 141422322, 370248452, 969323030, 2537720634, 6643838880, 17393796002, 45537549122, 119218851372, 312119004990, 817138163594, 2139295485800

Offset

1,1

Comments

Sequence extended to a(1) using the formula/recurrence (actual count for the 3-prism is 0, which reproduces A301775).

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Prism Graph

Index entries for linear recurrences with constant coefficients, signature (2, 1, 2, -1).

Formula

a(n) = A002878(n) + A131713(n).

a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).

G.f.: -2*x*(1+x)*(x^2-3*x-1) / ( (1+x+x^2)*(x^2-3*x+1) ).

Mathematica

Table[LucasL[2 n + 1] + 2 Cos[(2 n + 1) Pi/3], {n, 20}]
LinearRecurrence[{2, 1, 2, -1}, {2, 12, 30, 74}, 20]
CoefficientList[Series[-2 (-1 - 4 x - 2 x^2 + x^3)/(1 - 2 x - x^2 - 2 x^3 + x^4), {x, 0, 20}], x]

Crossrefs

Cf. A002878, A131713, A301775.

Sequence in context: A259127 A296257 A375623 * A286230 A083175 A019258

Adjacent sequences: A301771 A301772 A301773 * A301775 A301776 A301777

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 26 2018

Status

approved