cp's OEIS Frontend

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.

A167069 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {4, 5}}.

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%I A167069 #12 Aug 23 2023 10:17:53
%S A167069 3,1005,250848,60075885,14263332015,3379514561280,800337094071879,
%T A167069 189513130911442365,44873808170614072416,10625354802279238810125,
%U A167069 2515898969449422698378427,595720806457312484163072000,141056237447350542048435569739
%N A167069 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {4, 5}}.
%D A167069 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167069 P. Raff, <a href="/A167069/b167069.txt">Table of n, a(n) for n = 1..200</a>
%H A167069 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>, arXiv:0809.2551 [math.CO], 2008.
%H A167069 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-23-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167069 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167069 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 A167069 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A167069 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167069 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A167069 a(n) = 335 a(n-1)
%F A167069 - 26224 a(n-2)
%F A167069 + 744035 a(n-3)
%F A167069 - 10084457 a(n-4)
%F A167069 + 72968360 a(n-5)
%F A167069 - 295849710 a(n-6)
%F A167069 + 685799270 a(n-7)
%F A167069 - 909474816 a(n-8)
%F A167069 + 685799270 a(n-9)
%F A167069 - 295849710 a(n-10)
%F A167069 + 72968360 a(n-11)
%F A167069 - 10084457 a(n-12)
%F A167069 + 744035 a(n-13)
%F A167069 - 26224 a(n-14)
%F A167069 + 335 a(n-15)
%F A167069 - a(n-16)
%F A167069 G.f.: -3x(x^14 -2385x^12 +54940x^11 -451104x^10 +1542340x^9 -2024890x^8 +2024890x^6 -1542340x^5 +451104x^4 -54940x^3 +2385x^2 -1)/ (x^16 -335x^15 +26224x^14 -744035x^13 +10084457x^12 -72968360x^11 +295849710x^10 -685799270x^9 +909474816x^8 -685799270x^7 +295849710x^6 -72968360x^5 +10084457x^4 -744035x^3 +26224x^2 -335x +1).
%K A167069 nonn
%O A167069 1,1
%A A167069 _Paul Raff_