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A104400
Sums of 10 distinct positive pentatope numbers (A000332).
1
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
Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 05 2005
EXTENSIONS
Extended by Ray Chandler, Mar 05 2005
STATUS
approved