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

0,4

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).

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)

Prog

(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

Crossrefs

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

Sequence in context: A302921 A334692 A325474 * A133070 A135179 A397222

Adjacent sequences: A364648 A364649 A364650 * A364652 A364653 A364654

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 31 2023

Extensions

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

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

Status

approved