A367968 Number of 6-cycles in the n-Dorogovtsev-Goltsev-Mendes graph.

0, 0, 1, 38, 276, 1270, 4745, 15936, 50608, 156116, 474585, 1432450, 4309076, 12942618, 38847601, 116567660, 349733760, 1049238856, 3147761873, 9443339646, 28330082740, 84990322910, 254971055481, 764913266488, 2294739914096, 6884219872860, 20652659766505

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.

Eric Weisstein's World of Mathematics, Graph Cycle.

Index entries for linear recurrences with constant coefficients, signature (7, -18, 22, -13, 3).

Formula

a(n) = (65*3^n - 84*n - 6*n^2 - 40*n^3 - 65)/8.

a(n) = 7*a(n-1) - 18*a(n-2) + 22*a(n-3) - 13*a(n-4) + 3*a(n-5).

G.f.: -x^2*(1+31*x+28*x^2)/((-1+x)^4*(-1+3*x)).

Mathematica

Table[(65 3^n - 84 n - 6 n^2 - 40 n^3 - 65)/8, {n, 0, 20}]
LinearRecurrence[{7, -18, 22, -13, 3}, {0, 0, 1, 38, 276}, 20]

Crossrefs

Cf. A003462(n) (3-cycles), A290764(n-1) (4-cycles), A367967(n) (5-cycles).

Sequence in context: A160281 A186119 A007229 * A297799 A204070 A242209

Adjacent sequences: A367965 A367966 A367967 * A367969 A367970 A367971

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 06 2023

Status

approved