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%I M2557 #23 Feb 01 2022 15:07:52
%S 1,3,6,12,24,33,60,99,156,276,438,597,1134,1404,2904,3522,6876,7548,
%T 16680,18153,39846,41805
%N Cluster series for honeycomb.
%C 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
%D 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a003/A003204.java">Java program</a> (github)
%H M. F. Sykes and J. W. Essam, <a href="https://doi.org/10.1103/PhysRev.133.A310">Critical percolation probabilities by series methods</a>, Phys. Rev., 133 (1964), A310-A315.
%H M. F. Sykes and M. Glen, <a href="https://doi.org/10.1088/0305-4470/9/1/014">Percolation processes in two dimensions. I. Low-density series expansions</a>, J. Phys. A: Math. Gen., 9 (1976), 87-95.
%Y Cf. A001420, A003202 (triangular net), A003203 (square net), A003199 (bond percolation).
%K nonn,more
%O 0,2
%A _N. J. A. Sloane_
%E a(12)-a(18) from _Sean A. Irvine_, Aug 16 2020
%E a(19)-a(21) added from Sykes & Glen by _Andrey Zabolotskiy_, Feb 01 2022
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