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Search: id:A104395
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| 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
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1,1
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COMMENT
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Pentatope number Ptop(n) = binomial coefficient binomial(n,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.
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REFERENCES
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Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.
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LINKS
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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.
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FORMULA
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a(n) = Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive g=/=h=/=i=/=j=/=k and Ptop(n) = binomial coefficient binomial(n, 4).
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CROSSREFS
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Cf. A000332, A100009, A102857, A104392, A104393, A104394.
Sequence in context: A025380 A020342 A009944 this_sequence A109024 A063334 A102805
Adjacent sequences: A104392 A104393 A104394 this_sequence A104396 A104397 A104398
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 05 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) Mar 05 2005
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