A364651 Number of 6-cycles in the n-Pell graph.

0, 0, 0, 20, 206, 1282, 6302, 26942, 104948, 382444, 1325444, 4417024, 14263474, 44884286, 138222194, 417923290, 1243857480, 3651728760, 10592838440, 30403009612, 86440264694, 243689593114, 681776739174, 1894276352726, 5230101132028, 14357448589988

Offset: 0

Author

Eric W. Weisstein, Jul 31 2023

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Graph Cycle.
• Eric Weisstein's World of Mathematics, Pell Graph.
• Index entries for linear recurrences with constant coefficients, signature (8,-20,8,26,-8,-20,-8,-1).

Crossrefs

Cf. A290031, A364619 (number of 4-cycles).

Programs

PARI

seq(n) = Vec(2*x^3*(10 + 23*x + 17*x^2 + 3*x^3 - x^4)/(1 - 2*x - x^2)^4 + O(x*x^n), -n-1) \\ Andrew Howroyd, Jun 12 2025

Formula

From Andrew Howroyd, Jun 12 2025: (Start)

G.f.: 16*x^3*(1 + x)^3/(1 - 2*x - x^2)^4 + 2*x^3*(1 + x)*(2 + x)/(1 - 2*x - x^2)^3.

G.f.: 2*x^3*(10 + 23*x + 17*x^2 + 3*x^3 - x^4)/(1 - 2*x - x^2)^4. (End)

Extensions

a(10)-a(12) from Eric W. Weisstein, Dec 07 2023

a(13) onwards from Andrew Howroyd, Jun 12 2025