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A002709 Triangulations of the disk G_{n,0}.
(Formerly M3933 N1618)
11
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 p.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

Table of n, a(n) for n=0..21.

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

Adjacent sequences:  A002706 A002707 A002708 * A002710 A002711 A002712

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended by Max Alekseyev, Mar 30 2009

STATUS

approved

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Last modified February 16 21:12 EST 2019. Contains 320199 sequences. (Running on oeis4.)