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A002709 Triangulations of the disk G_{n,0}.
(Formerly M3933 N1618)
15
1, 1, 1, 5, 24, 133, 846, 5661, 39556, 286000, 2123329, 16112057, 124512556, 977227830, 7772368380, 62535450861, 508271324688, 4168218286276, 34455941596060, 286864341314320, 2403705165816240, 20258850167232165 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Apparently, also the number of regular flexagons of order 3(n+1) (see Oakley-Wisner link pp. 149-151). - Michel Marcus, Jun 23 2013
REFERENCES
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).
LINKS
William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768.
W. G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768. [Annotated scanned copy]
C. O. Oakley and R. J. Wisner, Flexagons, The American Mathematical Monthly, Vol. 64, No. 3 (Mar., 1957), pp. 143-154.
PROG
(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
CROSSREFS
A row or column of the array in A262586.
Sequence in context: A036919 A020067 A066118 * A193668 A009411 A080996
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended by Max Alekseyev, Mar 30 2009
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)