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A104396 Sums of 6 distinct positive pentatope numbers (A000332). 4
252, 336, 392, 427, 447, 456, 457, 461, 512, 547, 567, 577, 581, 596, 621, 631, 651, 661, 665, 677, 687, 707, 712, 717, 721, 732, 742, 746, 752, 756, 761, 772, 776, 786, 796, 816, 826, 830, 841, 852, 872, 881, 882, 886, 897, 907, 916, 917, 921, 932 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Pentatope number Ptop(n) = binomial(n+3,4) = n*(n+1)*(n+2)*(n+3)/24.

Hyun Kwang Kim asserts that every positive integer can be represented as the sum of no more than 8 pentatope numbers; but in this sequence we are only concerned with sums of nonzero distinct pentatope numbers.

REFERENCES

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.

LINKS

Table of n, a(n) for n=1..50.

Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.

J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.

Eric Weisstein's World of Mathematics, Pentatope Number.

FORMULA

a(n) = Ptop(f) + Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive f=/=g=/=h=/=i=/=j=/=k and Ptop(n) = binomial(n+3,4).

CROSSREFS

Cf. A000332, A100009, A102857, A104392, A104393, A104394, A104395.

Sequence in context: A045182 A046331 A066695 * A207373 A072443 A129623

Adjacent sequences:  A104393 A104394 A104395 * A104397 A104398 A104399

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 05 2005

EXTENSIONS

Extended by Ray Chandler, Mar 05 2005

STATUS

approved

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Last modified April 27 06:52 EDT 2017. Contains 285508 sequences.