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A002709
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Triangulations of the disk G_{n,0}.
(Formerly M3933 N1618)
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15
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1, 1, 1, 5, 24, 133, 846, 5661, 39556, 286000, 2123329, 16112057, 124512556, 977227830, 7772368380, 62535450861, 508271324688, 4168218286276, 34455941596060, 286864341314320, 2403705165816240, 20258850167232165
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OFFSET
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0,4
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COMMENTS
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Apparently, also the number of regular flexagons of order 3(n+1) (see Oakley-Wisner link pp. 149-151). - Michel Marcus, Jun 23 2013
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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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C. O. Oakley and R. J. Wisner, Flexagons, The American Mathematical Monthly, Vol. 64, No. 3 (Mar., 1957), pp. 143-154.
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PROG
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(PARI) a(n) = {if (n % 3 == 0, k = n/3; return (binomial(12*k-1, 3*k-1)/((6*k-1)*(12*k-1))); ); if (n % 3 == 1, k = (n-1)/3; return (binomial(12*k+3, 3*k)/(3*(4*k+1)*(6*k+1))+2*binomial(4*k, k)/(3*(3*k+1))); ); if (n % 3 == 2, k = (n-2)/3; return (binomial(12*k+7, 3*k+1)/(3*(2*k+1)*(12*k+7))+4*binomial(4*k+1, k)/(3*(3*k+2))); ); } \\ (number of regular flexagons of order 3*n) Michel Marcus, Jun 15 2013
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CROSSREFS
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A row or column of the array in A262586.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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