A104399 Sums of 9 distinct positive pentatope numbers (A000332).

1287, 1507, 1672, 1792, 1793, 1876, 1932, 1958, 1967, 1987, 1997, 2001, 2078, 2157, 2162, 2178, 2218, 2253, 2273, 2283, 2287, 2298, 2322, 2382, 2438, 2442, 2463, 2473, 2493, 2503, 2507, 2526, 2542, 2547, 2582, 2603, 2612, 2617, 2637, 2638, 2647, 2651

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..42.

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

Crossrefs

Cf. A000332, A100009, A102857, A104392, A104393, A104394, A104395, A104396, A104397, A104398.

Sequence in context: A270055 A252116 A084803 * A353347 A232253 A140914

Adjacent sequences: A104396 A104397 A104398 * A104400 A104401 A104402

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved