%I #21 Dec 14 2015 05:54:24

%S 2002,2288,2508,2652,2673,2793,2872,2877,2933,2968,2988,2998,3002,

%T 3037,3107,3157,3158,3241,3297,3323,3327,3332,3352,3362,3366,3443,

%U 3492,3527,3543,3583,3612,3613,3618,3638,3648,3652,3663,3667,3696,3747,3752,3778

%N Sums of 10 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 Robert Israel, <a href="/A104400/b104400.txt">Table of n, a(n) for n = 1..10000</a>

%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(b) + Ptop(c) + Ptop(d) + Ptop(e) + Ptop(f) + Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive b=/=c=/=d=/=e=/=f=/=g=/=h=/=i=/=j=/=k and Ptop(n) = binomial(n+3,4).

%p N:= 10000: # to get all terms <= N

%p nmax:= floor(-3/2+1/2*sqrt(5+4*sqrt(1+24*N))):

%p S:= select(`<=`,{seq(add(s*(s+1)*(s+2)*(s+3)/24,s=c),

%p c = combinat:-choose(nmax,10))},N):

%p sort(convert(S,list)); # _Robert Israel_, Dec 14 2015

%Y Cf. A000332, A100009, A102857, A104392, A104393, A104394, A104395, A104396, A104397, A104398, A104399.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 05 2005

%E Extended by _Ray Chandler_, Mar 05 2005