

A104395


Sums of 5 distinct positive pentatope numbers (A000332).


5



126, 182, 217, 237, 247, 251, 266, 301, 321, 331, 335, 357, 377, 386, 387, 391, 412, 421, 422, 426, 441, 442, 446, 451, 455, 456, 477, 497, 507, 511, 532, 542, 546, 551, 561, 562, 566, 576, 581, 586, 591, 595, 606, 616, 620, 626, 630, 642, 646, 650
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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: SpringerVerlag, pp. 5557, 1996.


LINKS

Table of n, a(n) for n=1..50.
Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 6575.
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
Eric Weisstein's World of Mathematics, Pentatope Number.


FORMULA

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


CROSSREFS

Cf. A000332, A100009, A102857, A104392, A104393, A104394.
Sequence in context: A179482 A009944 A203566 * A267331 A267739 A254370
Adjacent sequences: A104392 A104393 A104394 * A104396 A104397 A104398


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Mar 05 2005


EXTENSIONS

Extended by Ray Chandler, Mar 05 2005


STATUS

approved



