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

1,2

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).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A301774.

Sequence in context: A110019 A069486 A211117 * A175157 A371075 A286659

Adjacent sequences: A301772 A301773 A301774 * A301776 A301777 A301778

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 26 2018

Extensions

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

Status

approved