This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104392 #19 Feb 16 2025 08:32:56
%S A104392 6,16,20,36,40,50,71,75,85,105,127,131,141,161,196,211,215,225,245,
%T A104392 280,331,335,336,345,365,400,456,496,500,510,530,540,565,621,705,716,
%U A104392 720,730,750,785,825,841,925,1002,1006,1016,1036,1045,1071,1127
%N A104392 Sums of 2 distinct positive pentatope numbers (A000332).
%C A104392 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 A104392 Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.
%H A104392 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 A104392 J. V. Post, <a href="http://www.magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>.
%H A104392 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentatopeNumber.html">Pentatope Number</a>.
%F A104392 a(n) = Ptop(i) + Ptop(j) for some positive i=/=j and Ptop(n) = binomial(n+3,4).
%t A104392 nn=15; Select[Union[Total/@Subsets[Binomial[Range[4,nn],4],{2}]], #<Binomial[nn,4]+1&] (* _Harvey P. Dale_, Mar 13 2011 *)
%Y A104392 Cf. A000332, A100009, A102856.
%K A104392 easy,nonn
%O A104392 0,1
%A A104392 _Jonathan Vos Post_, Mar 05 2005
%E A104392 Extended by _Ray Chandler_, Mar 05 2005