A104399 -id:A104399 - cp's OEIS frontend

A104400 Sums of 10 distinct positive pentatope numbers (A000332).

2002, 2288, 2508, 2652, 2673, 2793, 2872, 2877, 2933, 2968, 2988, 2998, 3002, 3037, 3107, 3157, 3158, 3241, 3297, 3323, 3327, 3332, 3352, 3362, 3366, 3443, 3492, 3527, 3543, 3583, 3612, 3613, 3618, 3638, 3648, 3652, 3663, 3667, 3696, 3747, 3752, 3778

Offset: 1

Jonathan Vos Post, Mar 05 2005

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.

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.

Robert Israel, Table of n, a(n) for n = 1..10000
Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
Eric Weisstein's World of Mathematics, Pentatope Number.

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

N:= 10000: # to get all terms <= N
nmax:= floor(-3/2+1/2*sqrt(5+4*sqrt(1+24*N))):
S:= select(`<=`,{seq(add(s*(s+1)*(s+2)*(s+3)/24,s=c),
     c = combinat:-choose(nmax,10))},N):
sort(convert(S,list)); # Robert Israel, Dec 14 2015

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).

Extended by Ray Chandler, Mar 05 2005

cp's OEIS Frontend

A104400 Sums of 10 distinct positive pentatope numbers (A000332).

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