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Search: id:A104393
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| 21, 41, 51, 55, 76, 86, 90, 106, 110, 120, 132, 142, 146, 162, 166, 176, 197, 201, 211, 216, 226, 230, 231, 246, 250, 260, 281, 285, 295, 315, 336, 337, 341, 346, 350, 351, 366, 370, 371, 380, 401, 405, 406, 415, 435, 457, 461, 471, 491, 501
(list; graph; listen)
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OFFSET
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0,1
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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(i) + Ptop(j) + Ptop(k) for some positive 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.
Sequence in context: A020220 A084856 A070666 this_sequence A067344 A053428 A123842
Adjacent sequences: A104390 A104391 A104392 this_sequence A104394 A104395 A104396
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.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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