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%I #19 Dec 14 2015 05:54:45
%S 252,336,392,427,447,456,457,461,512,547,567,577,581,596,621,631,651,
%T 661,665,677,687,707,712,717,721,732,742,746,752,756,761,772,776,786,
%U 796,816,826,830,841,852,872,881,882,886,897,907,916,917,921,932
%N Sums of 6 distinct positive pentatope numbers (A000332).
%C Pentatope number Ptop(n) = binomial(n+3,4) = n*(n+1)*(n+2)*(n+3)/24.
%C 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.
%D Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.
%H Hyun Kwang Kim, <a href="http://dx.doi.org/10.1090/S0002-9939-02-06710-2">On Regular Polytope Numbers</a>, Proc. Amer. Math. Soc., 131 (2003), 65-75.
%H J. V. Post, <a href="http://www.magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentatopeNumber.html">Pentatope Number</a>.
%F 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(n+3,4).
%Y Cf. A000332, A100009, A102857, A104392, A104393, A104394, A104395.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 05 2005
%E Extended by _Ray Chandler_, Mar 05 2005
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