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Number of (undirected) Hamiltonian paths on the n-prism graph.
1

%I #10 Jun 20 2021 11:45:27

%S 30,72,130,228,350,528,738,1020,1342,1752,2210,2772,3390,4128,4930,

%T 5868,6878,8040,9282,10692,12190,13872,15650,17628,19710,22008,24418,

%U 27060,29822,32832,35970,39372,42910,46728,50690,54948,59358,64080,68962,74172,79550

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

%H Colin Barker, <a href="/A308137/b308137.txt">Table of n, a(n) for n = 3..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

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

%F From _Colin Barker_, Jul 19 2019: (Start)

%F 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).

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

%F 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.

%F (End)

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

%o (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

%Y Cf. A124350.

%K nonn,easy

%O 3,1

%A _Eric W. Weisstein_, May 14 2019

%E More terms from _Colin Barker_, Jul 19 2019