

A003203


Cluster series for square lattice.
(Formerly M3433)


16



1, 4, 12, 24, 52, 108, 224, 412, 844, 1528, 3152, 5036, 11984, 15040, 46512, 34788, 197612, 4036, 929368, 702592, 4847552, 7033956, 27903296, 54403996, 170579740
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OFFSET

0,2


COMMENTS

The word "cluster" here essentially means polyomino or animal. This sequence can be computed based on a calculation of the perimeter polynomials of polyominoes. In particular, if P_n(x) is the perimeter polynomial for all fixed polyominoes of size n, then this sequence is the coefficients of x in Sum_{k>=1} k^2 * x^k * P_k(1x).  Sean A. Irvine, Aug 15 2020


REFERENCES

J. W. Essam, Percolation and cluster size, in C. Domb and M. S. Green, Phase Transitions and Critical Phenomena, Ac. Press 1972, Vol. 2; see especially pp. 225226.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



CROSSREFS



KEYWORD

sign,more


AUTHOR



EXTENSIONS



STATUS

approved



