A104393 - OEIS

%I #15 Feb 14 2018 11:46:56

%S 21,41,51,55,76,86,90,106,110,120,132,142,146,162,166,176,197,201,211,

%T 216,226,230,231,246,250,260,281,285,295,315,336,337,341,346,350,351,

%U 366,370,371,380,401,405,406,415,435,457,461,471,491,501

%N Sums of 3 distinct positive pentatope numbers (A000332).

%C Pentatope number Ptop(n) = binomial(n+3,4) = 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.

%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(i) + Ptop(j) + Ptop(k) for some positive i=/=j=/=k and Ptop(n) = binomial(n+3,4).

%t Total/@Subsets[Table[Binomial[n+3,4],{n,10}],{3}]//Sort (* _Harvey P. Dale_, Feb 14 2018 *)

%Y Cf. A000332, A100009, A102857, A104392.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Mar 05 2005

%E Extended by _Ray Chandler_, Mar 05 2005