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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 (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..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(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

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Last modified April 25 00:32 EDT 2017. Contains 285346 sequences.