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A307939 Number of (undirected) Hamiltonian paths in the n-dipyramidal graph. 1

%I

%S 36,120,310,660,1218,2032,3150,4620,6490,8808,11622,14980,18930,23520,

%T 28798,34812,41610,49240,57750,67188,77602,89040,101550,115180,129978,

%U 145992,163270,181860,201810,223168,245982,270300,296170,323640,352758,383572,416130,450480

%N Number of (undirected) Hamiltonian paths in the n-dipyramidal graph.

%H Colin Barker, <a href="/A307939/b307939.txt">Table of n, a(n) for n = 3..1000</a>

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

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 2*n*(31 - 20*n + 4*n^2) for n > 3.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 7.

%F G.f.: 2*x^3*(18 - 12*x + 23*x^2 - 2*x^3 - 3*x^4) / (1 - x)^4. - _Colin Barker_, May 09 2019

%t Join[{36}, Table[2 n (31 - 20 n + 4 n^2), {n, 4, 20}]]

%t Join[{36}, LinearRecurrence[{4, -6, 4, -1}, {120, 310, 660, 1218}, 20]]

%t CoefficientList[Series[-2 (-18 + 12 x - 23 x^2 + 2 x^3 + 3 x^4)/(-1 + x)^4, {x, 0, 20}], x]

%o (PARI) Vec(2*x^3*(18 - 12*x + 23*x^2 - 2*x^3 - 3*x^4) / (1 - x)^4 + O(x^40)) \\ _Colin Barker_, May 09 2019

%K nonn,easy

%O 3,1

%A _Eric W. Weisstein_, May 06 2019

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Last modified August 3 08:21 EDT 2021. Contains 346435 sequences. (Running on oeis4.)