A397461 Number of paths in the n-Cameron graph.

3, 1175, 37935, 780495, 13277235, 204605927, 2980041263, 41961830399, 578751842795, 7880615412799, 106455838015359, 1430986454530607, 19176915377640787, 256513258632515831, 3427243905233672255, 45759272738186233567, 610704810487832671307, 8148435627671334850543, 108705546897434729803599

Offset

0,1

Comments

The n-Cameron graph is defined for n >= 1. The sequence has been extended to a(0) using the recurrence. - Andrew Howroyd, Jul 05 2026

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Cameron Graph.

Eric Weisstein's World of Mathematics, Graph Path.

Index entries for linear recurrences with constant coefficients, signature (29,-274,884,-93,-1697,2156,-3468,4816,-3120,832,-64)

Formula

G.f.: (3 + 1088*x + 4682*x^2 - 322*x^3 - 1351*x^4 + 1568*x^5 - 10348*x^6 + 20864*x^7 - 16720*x^8 + 5504*x^9 - 576*x^10)/((1 - x)^2*(1 - 8*x + 4*x^2)^2*(1 - 11*x - 29*x^2 - 27*x^3 - 28*x^4 + 4*x^5)). - Andrew Howroyd, Jul 05 2026

Example

a(1) = 1175 since the 1-Cameron graph has 1175 paths.

Crossrefs

Cf. A387375 (number of cycles in the same graph).

Cf. A387438 (number of Hamiltonian paths in the same graph).

Sequence in context: A096082 A274994 A178195 * A199236 A171360 A034315

Adjacent sequences: A397456 A397457 A397460 * A397462 A397463 A397464

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 26 2026

Extensions

a(0) prepended and a(7) onward from Andrew Howroyd, Jul 05 2026

Status

approved