OFFSET
0,2
COMMENTS
The word "cluster" here essentially means polyiamond. This sequence can be computed based on a calculation of the perimeter polynomials of polyiamonds. In particular, if P_n(x) is the perimeter polynomial for all fixed polyiamonds of size n, then this sequence is the coefficients of x in Sum_{k>=1} k^2 * x^k * P_k(1-x). - Sean A. Irvine, Aug 16 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. 225-226.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Sean A. Irvine, Java program (github)
M. F. Sykes and J. W. Essam, Critical percolation probabilities by series methods, Phys. Rev., 133 (1964), A310-A315.
M. F. Sykes and M. Glen, Percolation processes in two dimensions. I. Low-density series expansions, J. Phys. A: Math. Gen., 9 (1976), 87-95.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(12)-a(18) from Sean A. Irvine, Aug 16 2020
a(19)-a(21) added from Sykes & Glen by Andrey Zabolotskiy, Feb 01 2022
STATUS
approved