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A003204
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Cluster series for honeycomb.
(Formerly M2557)
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6
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1, 3, 6, 12, 24, 33, 60, 99, 156, 276, 438, 597, 1134, 1404, 2904, 3522, 6876, 7548, 16680, 18153, 39846, 41805
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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