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 A104393 Sums of 3 distinct positive pentatope numbers (A000332). 7
 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; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. REFERENCES Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996. LINKS 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(i) + Ptop(j) + Ptop(k) for some positive i=/=j=/=k and Ptop(n) = binomial coefficient binomial(n, 4). CROSSREFS Cf. A000332, A100009, A102857, A104392. Sequence in context: A020220 A084856 A070666 * A215145 A154576 A173960 Adjacent sequences:  A104390 A104391 A104392 * A104394 A104395 A104396 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Mar 05 2005 EXTENSIONS Extended by Ray Chandler Mar 05 2005 STATUS approved

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