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A169895 Number of n-faced simplicial decompositions on a cylinder. 0
21, 264, 2134, 14108, 83072, 453812, 2352872, 11740144, 56894391, 269476772, 1253108594, 5740109460, 25966561036, 116231267108, 515605930368, 2269542200416, 9922528937450, 43125192822720, 186450920282476, 802370755873080, 3438559602598096, 14680863523207304 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

LINKS

Table of n, a(n) for n=6..27.

Juanjo Rué, Enumeration and limit laws of dissections on a cylinder, Discrete Math., 310 (2010), 2519-2541.

FORMULA

The reference gives an explicit g.f.

PROG

(PARI)

acyl(m)={

  my( x='x+O('x^(m+3)), Cx, Nx, Dx, Hx );

  Cx = (1 - sqrt(1-4*x))/(2*x);  /* g.f. of the Catalan numbers (A000108) */

  Nx = ((-8*x^5+18*x^4-52*x^3+20*x^2+2*x-1)*Cx + (8*x^5-2*x^4+33*x^3-20*x^2-x+1));

  Dx = (x*(1-4*x)^2);

  Hx = Nx/Dx;

  for(n=0, m, print1(polcoeff(Hx, n, 'x), ", "));

} /* Michel Marcus, Feb 06 2013 */

CROSSREFS

Sequence in context: A135122 A231380 A045505 * A092794 A133717 A056282

Adjacent sequences:  A169892 A169893 A169894 * A169896 A169897 A169898

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 26 2010

EXTENSIONS

More terms from Michel Marcus, Feb 06 2013

STATUS

approved

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Last modified October 1 07:48 EDT 2020. Contains 337442 sequences. (Running on oeis4.)