A104396 Sums of 6 distinct positive pentatope numbers (A000332).

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

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: A046331 A066695 A372755 * A207373 A072443 A129623

Adjacent sequences: A104393 A104394 A104395 * A104397 A104398 A104399

Keyword

easy,nonn,changed

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved