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

Author

Eric W. Weisstein, Dec 06 2023

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

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

Programs

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]

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)).