

A007175


Number of simplicial 4clusters 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
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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), 203217.
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



