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Search: id:A104396
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| 252, 336, 392, 427, 447, 456, 457, 461, 512, 547, 567, 577, 581, 596, 621, 631, 651, 661, 665, 677, 687, 707, 712, 717, 721, 732, 742, 746, 752, 756, 761, 772, 776, 786, 796, 816, 826, 830, 841, 852, 872, 881, 882, 886, 897, 907, 916, 917, 921, 932
(list; graph; listen)
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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(f) + Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive f=/=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, A104395.
Sequence in context: A045182 A046331 A066695 this_sequence A072443 A129623 A062904
Adjacent sequences: A104393 A104394 A104395 this_sequence A104397 A104398 A104399
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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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