A387438 Number of Hamiltonian paths in the n-Cameron graph.

2, 106, 614, 2658, 10406, 39298, 146618, 544858, 2022242, 7502602, 27831590, 103240050, 382960198, 1420553730, 5269401338, 19546309418, 72505044994, 268950077226, 997642902822, 3700654671362, 13727201336742, 50919654289410, 188881267873530, 700635812456570, 2598937137713634

Offset

0,1

Comments

The number of Hamiltonian cycles is 3 for every n > 0. - Andrew Howroyd, Aug 31 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Cameron Graph.

Eric Weisstein's World of Mathematics, Hamiltonian Path.

Index entries for linear recurrences with constant coefficients, signature (5,-5,1,-1,1,-1,1).

Formula

G.f.: 2*(1 + 48*x + 47*x^2 + 58*x^3 + 41*x^4 + 24*x^5 + 5*x^6)/((1 - x)^2*(1 - 3*x - 2*x^2 - 2*x^3 - x^4 - x^5)). - Andrew Howroyd, Aug 31 2025

a(n) = 5*a(n-1)-5*a(n-2)+a(n-3)-a(n-4)+a(n-5)-a(n-6)+a(n-7). - Eric W. Weisstein, Aug 31 2025

Mathematica

Table[(7 - 112 (n + 1) + 1/938 RootSum[-1 - # - 2 #^2 - 2 #^3 - 3 #^4 + #^5 &, -3391 #^n - 6806 #^(n + 1) - 7388 #^(n + 2) - 1846 #^(n + 3) + 1745 #^(n + 4) &])/2, {n, 0, 20}]
LinearRecurrence[{5, -5, 1, -1, 1, -1, 1}, {106, 614, 2658, 10406, 39298, 146618, 544858}, {0, 20}]
CoefficientList[Series[-(2 (1 + 48 x + 47 x^2 + 58 x^3 + 41 x^4 + 24 x^5 + 5 x^6)/((-1 + x)^2 (-1 + 3 x + 2 x^2 + 2 x^3 + x^4 + x^5))), {x, 0, 20}], x]

Crossrefs

Cf. A387375.

Sequence in context: A229016 A222840 A356723 * A260579 A125593 A352496

Adjacent sequences: A387435 A387436 A387437 * A387439 A387440 A387441

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 29 2025

Extensions

a(0) prepended and a(6) onwards from Andrew Howroyd, Aug 31 2025

Status

approved