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

1,1

Comments

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.

References

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

Links

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.

Formula

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).

Maple

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

Crossrefs

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

Sequence in context: A125680 A162238 A162239 * A250880 A154049 A339803

Adjacent sequences: A104397 A104398 A104399 * A104401 A104402 A104403

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved