OFFSET
1,1
COMMENTS
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.
Eric Weisstein's World of Mathematics, Pentatope Number.
FORMULA
a(n) = Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive g=/=h=/=i=/=j=/=k and Ptop(n) = binomial(n+3,4).
MAPLE
N:= 1000: # for terms <= N
ptop:= n -> n*(n+1)*(n+2)*(n+3)/24:
P:= 1:
for i from 1 while ptop(i) < N do
P:= P * (1 + x*y^ptop(i))
od:
sort(map(degree, convert(convert(series(coeff(P, x, 5), y, N+1), polynom), list)));
# Robert Israel, Nov 20 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 05 2005
EXTENSIONS
Extended by Ray Chandler, Mar 05 2005
STATUS
approved