A007175 Number of simplicial 4-clusters with n cells. (Formerly M2762)

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

Offset

1,4

Comments

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

References

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.

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

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 A330527

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