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A308137 Number of (undirected) Hamiltonian paths on the n-prism graph. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

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).

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)

PROG

(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

CROSSREFS

Cf. A124350.

Sequence in context: A071142 A218327 A259753 * A179321 A039517 A185479

Adjacent sequences:  A308134 A308135 A308136 * A308138 A308139 A308140

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, May 14 2019

EXTENSIONS

More terms from Colin Barker, Jul 19 2019

STATUS

approved

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Last modified January 22 13:36 EST 2020. Contains 331149 sequences. (Running on oeis4.)