This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A308137 #11 Feb 16 2025 08:33:55
%S A308137 30,72,130,228,350,528,738,1020,1342,1752,2210,2772,3390,4128,4930,
%T A308137 5868,6878,8040,9282,10692,12190,13872,15650,17628,19710,22008,24418,
%U A308137 27060,29822,32832,35970,39372,42910,46728,50690,54948,59358,64080,68962,74172,79550
%N A308137 Number of (undirected) Hamiltonian paths on the n-prism graph.
%H A308137 Colin Barker, <a href="/A308137/b308137.txt">Table of n, a(n) for n = 3..1000</a>
%H A308137 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H A308137 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A308137 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A308137 a(n) = A124350(n)/2.
%F A308137 From _Colin Barker_, Jul 19 2019: (Start)
%F A308137 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 A308137 a(n) = n*(3 + (-1)^n + 2*n^2) / 2.
%F A308137 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 A308137 (End)
%t A308137 LinearRecurrence[{2,1,-4,1,2,-1},{30,72,130,228,350,528},50] (* _Harvey P. Dale_, Jun 20 2021 *)
%o A308137 (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 A308137 Cf. A124350.
%K A308137 nonn,easy
%O A308137 3,1
%A A308137 _Eric W. Weisstein_, May 14 2019
%E A308137 More terms from _Colin Barker_, Jul 19 2019