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%I #24 Nov 26 2015 21:31:24
%S 1,144,264,724,2097,6388,20168,65416,216286,725208,2457738,8398428,
%T 28882214,99811780,346190276,1203840960,4193106473,14616481492,
%U 50950086836,177468099920,617261864317,2142475178740,7416625966122,25592444012160,87988338886088
%N Number of connected subgraphs of the 12 X 12 grid graph induced by a vertex subset of size n.
%C A sequence of this type is known as the "spectrum" in the network reliability literature (see Gertsbakh 2009).
%C This sequence was computed using the transfer matrix method.
%H Rohan Shah, <a href="/A262245/b262245.txt">Table of n, a(n) for n = 0..144</a>
%H N. Clisby, I. Jensen, <a href="http://dx.doi.org/10.1088/1751-8113/45/11/115202">A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice</a>, Journal of Physics A: Mathematical and Theoretical 45(11) 2012.
%H I. B. Gertsbakh and Y. Shpungin, <a href="http://dx.doi.org/10.1201/b12536-11">Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo</a>, Boca Raton, FL, USA: CRC Press, Inc., 2009.
%H D. J. Klein, G. E. Hite, T. G. Schmalz, <a href="http://dx.doi.org/10.1002/jcc.540070407">Transfer-matrix method for subgraph enumeration: Applications to polypyrene fusenes</a>, Journal of Computational Chemistry 7(4):443-456 1986.
%H Rohan Shah, <a href="https://github.com/rohan-shah/residualConnectivity">Transfer matrix code (written in C++) used to generate this sequence</a>.
%e a(0) = a(|V|) = 1 as (V, E) is connected.
%e a(1) = a(|V| - 1) = |V| as (V, E) is connected.
%e a(142) = binomial(144,2) - 4.
%K nonn,full,fini
%O 0,2
%A _Rohan Shah_, Sep 15 2015
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