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A122652
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a(0) = 0, a(1) = 4; for n > 1, a(n) = 10*a(n-1) - a(n-2).
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4
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0, 4, 40, 396, 3920, 38804, 384120, 3802396, 37639840, 372596004, 3688320200, 36510605996, 361417739760, 3577666791604, 35415250176280, 350574834971196, 3470333099535680, 34352756160385604, 340057228504320360, 3366219528882817996, 33322138060323859600
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OFFSET
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0,2
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COMMENTS
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Kekulé numbers for the benzenoids P_2(n).
Numbers n such that 6*n^2 + 4 is a square. - Colin Barker, Mar 17 2014
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 283, K{P_2(n)}).
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LINKS
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Andersen, K., Carbone, L. and Penta, D., Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields, Journal of Number Theory and Combinatorics, Vol 2, No. 3 pp 245-278, 2011. See Section 9.
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FORMULA
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a(n) = (2*arcsinh(sqrt(2))*sinh(2*n*arcsinh(sqrt(2)))/log(sqrt(2) + sqrt(3)))/sqrt(6). - Artur Jasinski, Aug 09 2016
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<2, (n%2)*4, 10*a(n-1)-a(n-2)) \\ Benoit Cloitre, Sep 23 2006
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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