A007175 Number of simplicial 4-clusters with n cells.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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

Programs

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 *)

Extensions

More terms from Robert A. Russell, Apr 20 2012