A104392 - OEIS

%I #18 Dec 14 2015 05:55:11

%S 6,16,20,36,40,50,71,75,85,105,127,131,141,161,196,211,215,225,245,

%T 280,331,335,336,345,365,400,456,496,500,510,530,540,565,621,705,716,

%U 720,730,750,785,825,841,925,1002,1006,1016,1036,1045,1071,1127

%N Sums of 2 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) for some positive i=/=j and Ptop(n) = binomial(n+3,4).

%t nn=15; Select[Union[Total/@Subsets[Binomial[Range[4,nn],4],{2}]], #<Binomial[nn,4]+1&]  (* _Harvey P. Dale_, Mar 13 2011 *)

%Y Cf. A000332, A100009, A102856.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Mar 05 2005

%E Extended by _Ray Chandler_, Mar 05 2005