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

Author

Eric W. Weisstein, Mar 26 2018

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

Cf. A002878, A131713, A301775.

Programs

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]

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) ).