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A007175 Number of simplicial 4-clusters with n cells.
(Formerly M2762)
2
1, 1, 1, 3, 8, 40, 211, 1406, 9754, 71591, 537699, 4131943, 32271490, 255690412, 2050376883, 16616721067, 135920429975, 1120999363012, 9313779465810, 77897862860818, 655433405297407, 5544948758579214, 47143948331898873, 402655164736641843, 3453509765971944236, 29734988097830504532 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Hering article has error in the 20th term. - Robert A. Russell, Apr 20 2012

REFERENCES

F. Hering et al., The enumeration of stack polytopes and simplicial clusters, Discrete Math., 40 (1982), 203-217.

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=1..26.

MATHEMATICA

Table[Binomial[4 n, n]/(12 (3 n + 1) (3 n + 2)) +

  If[EvenQ[n],

   Binomial[2 n, n/2]/(8 (3 n/2 + 1)) +

    Binomial[2 n - 1, n/2 - 1]/((3 n/2 + 1)),

   Binomial[2 n - 1, n/2 - 1/2]/(2 (3 n/2 + 1/2))] +

  Switch[Mod[n, 3], 0, Binomial[4 n/3, n/3]/(3 (n + 1)), 1,

   2 Binomial[4 n/3 - 1/3, n/3 - 1/3]/(3 (n + 1)), 2,

   Binomial[4 n/3 - 2/3, n/3 - 2/3]/(n + 1)] +

  If[2 == Mod[n, 4], Binomial[n - 1, n/4 - 1/2]/(2 (3 n/4 + 1/2)), 0] +

  If[1 == Mod[n, 5], 2 Binomial[4 n/5 - 4/5, n/5 - 1/5]/(5 (3 n/5 + 2/5)),

   0], {n, 1, 30}] (* Robert A. Russell, Apr 20 2012 *)

CROSSREFS

Sequence in context: A262126 A110561 A107991 * A152394 A168468 A224246

Adjacent sequences:  A007172 A007173 A007174 * A007176 A007177 A007178

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Robert A. Russell, Apr 20 2012

STATUS

approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)