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 A003691 #34 Mar 19 2023 05:00:13 %S A003691 3,36,324,2880,25632,228096,2029824,18063360,160745472,1430470656, %T A003691 12729729024,113281597440,1008090611712,8970977673216,79832546279424, %U A003691 710428191621120 %N A003691 Number of spanning trees with degrees 1 and 3 in K_3 X P_2n. %D A003691 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154. %H A003691 Vincenzo Librandi, <a href="/A003691/b003691.txt">Table of n, a(n) for n = 1..1000</a> %H A003691 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154. %H A003691 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a> %H A003691 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a> %H A003691 <a href="/index/Tra#trees">Index entries for sequences related to trees</a> %H A003691 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,8). %F A003691 a(n) = 8*a(n-1) + 8*a(n-2), n>3. %F A003691 From _Bruno Berselli_, Aug 02 2011: (Start) %F A003691 G.f.: 3*x*(1+2*x)^2/(1-8*x-8*x^2). %F A003691 For n>1, a(n) = 3*sqrt(3)*sqrt(2^(2*n-7))*((2+sqrt(6))^n-(2-sqrt(6))^n). (End) %o A003691 (Magma) i:=[3,36,324]; [n le 3 select i[n] else 8*(Self(n-1)+Self(n-2)): n in [1..16]]; // _Bruno Berselli_, Aug 02 2011 %o A003691 (PARI) a(n)=([0,1; 8,8]^(n-1)*[3;36])[1,1] \\ _Charles R Greathouse IV_, Jun 23 2020 %Y A003691 Cf. A057091. %K A003691 nonn,easy %O A003691 1,1 %A A003691 _Frans J. Faase_