

A262245


Number of connected subgraphs of the 12 X 12 grid graph induced by a vertex subset of size n.


1



1, 144, 264, 724, 2097, 6388, 20168, 65416, 216286, 725208, 2457738, 8398428, 28882214, 99811780, 346190276, 1203840960, 4193106473, 14616481492, 50950086836, 177468099920, 617261864317, 2142475178740, 7416625966122, 25592444012160, 87988338886088
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OFFSET

0,2


COMMENTS

A sequence of this type is known as the "spectrum" in the network reliability literature (see Gertsbakh 2009).
This sequence was computed using the transfer matrix method.


LINKS

Rohan Shah, Table of n, a(n) for n = 0..144
N. Clisby, I. Jensen, A new transfermatrix algorithm for exact enumerations: selfavoiding polygons on the square lattice, Journal of Physics A: Mathematical and Theoretical 45(11) 2012.
I. B. Gertsbakh and Y. Shpungin, Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo, Boca Raton, FL, USA: CRC Press, Inc., 2009.
D. J. Klein, G. E. Hite, T. G. Schmalz, Transfermatrix method for subgraph enumeration: Applications to polypyrene fusenes, Journal of Computational Chemistry 7(4):443456 1986.
Rohan Shah, Transfer matrix code (written in C++) used to generate this sequence.


EXAMPLE

a(0) = a(V) = 1 as (V, E) is connected.
a(1) = a(V  1) = V as (V, E) is connected.
a(142) = binomial(144,2)  4.


CROSSREFS

Sequence in context: A064563 A008436 A250773 * A134341 A125841 A320457
Adjacent sequences: A262242 A262243 A262244 * A262246 A262247 A262248


KEYWORD

nonn,full,fini


AUTHOR

Rohan Shah, Sep 15 2015


STATUS

approved



