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A104399 Sums of 9 distinct positive pentatope numbers (A000332). 1
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 (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..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 * A232253 A140914 A239436

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

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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.