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A104395
Sums of 5 distinct positive pentatope numbers (A000332).
6
126, 182, 217, 237, 247, 251, 266, 301, 321, 331, 335, 357, 377, 386, 387, 391, 412, 421, 422, 426, 441, 442, 446, 451, 455, 456, 477, 497, 507, 511, 532, 542, 546, 551, 561, 562, 566, 576, 581, 586, 591, 595, 606, 616, 620, 626, 630, 642, 646, 650
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
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