A308137 Number of (undirected) Hamiltonian paths on the n-prism graph.

30, 72, 130, 228, 350, 528, 738, 1020, 1342, 1752, 2210, 2772, 3390, 4128, 4930, 5868, 6878, 8040, 9282, 10692, 12190, 13872, 15650, 17628, 19710, 22008, 24418, 27060, 29822, 32832, 35970, 39372, 42910, 46728, 50690, 54948, 59358, 64080, 68962, 74172, 79550

Offset: 3

Author

Eric W. Weisstein, May 14 2019

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 3..1000
• Eric Weisstein's World of Mathematics, Hamiltonian Path
• Eric Weisstein's World of Mathematics, Prism Graph
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A124350.

Programs

Mathematica

LinearRecurrence[{2,1,-4,1,2,-1},{30,72,130,228,350,528},50] (* Harvey P. Dale, Jun 20 2021 *)

PARI

Vec(2*x^3*(15 + 6*x - 22*x^2 + 8*x^3 + 11*x^4 - 6*x^5) / ((1 - x)^4*(1 + x)^2) + O(x^30)) \\ Colin Barker, Jul 19 2019

Formula

a(n) = A124350(n)/2.

From Colin Barker, Jul 19 2019: (Start)

G.f.: 2*x^3*(15 + 6*x - 22*x^2 + 8*x^3 + 11*x^4 - 6*x^5) / ((1 - x)^4*(1 + x)^2).

a(n) = n*(3 + (-1)^n + 2*n^2) / 2.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>8.

(End)

Extensions

More terms from Colin Barker, Jul 19 2019