A301775 Number of odd chordless cycles in the (2n+1)-web graph.

0, 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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Chordless Cycle
• Eric Weisstein's World of Mathematics, Web Graph
• Index entries for linear recurrences with constant coefficients, signature (2,1,2,-1).

Crossrefs

Cf. A301774.

Programs

Magma

I:=[0,12,30,74,200]; [n le 5 select I[n] else  2*Self(n-1)+Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Mar 27 2018

Mathematica

Rest @ CoefficientList[Series[2 x^2*(6 + 3 x + x^2 - x^3)/((1 - 3 x + x^2) (1 + x + x^2)), {x, 0, 29}], x] (* Michael De Vlieger, Mar 26 2018 *)
Join[{0}, LinearRecurrence[{2, 1, 2, -1}, {12, 30, 74, 200}, 30]] (* Vincenzo Librandi, Mar 27 2018 *)
Join[{0}, Table[LucasL[2 n + 1] + Cos[2 n Pi/3] - Sqrt[3] Sin[2 n Pi/3], {n, 2, 20}]] (* Eric W. Weisstein, Mar 27 2018 *)

PARI

Vec(2*(6 + 3*x + x^2 - x^3)/((1 - 3*x + x^2)*(1 + x + x^2)) + O(x^30)) \\ Andrew Howroyd, Mar 26 2018

Formula

From Andrew Howroyd, Mar 26 2018: (Start)

a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4) for n > 5.

G.f.: 2*x^2*(6 + 3*x + x^2 - x^3)/((1 - 3*x + x^2)*(1 + x + x^2)).

(End)

a(n) = A002878(n) + cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3) for n > 1. - Eric W. Weisstein, Mar 27 2018

a(n) = A002878(n) + A131713(n), n>1. - R. J. Mathar, Apr 17 2018

Extensions

Terms a(10) and beyond from Andrew Howroyd, Mar 26 2018