A104394 Sums of 4 distinct positive pentatope numbers (A000332).

56, 91, 111, 121, 125, 147, 167, 177, 181, 202, 212, 216, 231, 232, 236, 246, 251, 261, 265, 286, 296, 300, 316, 320, 330, 342, 351, 352, 356, 371, 372, 376, 381, 385, 386, 406, 407, 411, 416, 420, 421, 436, 440, 441, 450, 462, 472, 476, 492, 496

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

Crossrefs

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

Sequence in context: A286981 A254369 A234927 * A353281 A101935 A101294

Adjacent sequences: A104391 A104392 A104393 * A104395 A104396 A104397

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved