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A104398
Sums of 8 distinct positive pentatope numbers (A000332).
2
792, 957, 1077, 1161, 1177, 1217, 1252, 1272, 1282, 1286, 1297, 1381, 1437, 1462, 1463, 1472, 1492, 1502, 1506, 1546, 1583, 1602, 1637, 1657, 1666, 1667, 1671, 1722, 1723, 1748, 1757, 1758, 1777, 1778, 1787, 1788, 1791, 1792, 1806, 1827, 1832, 1841
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(d) + Ptop(e) + Ptop(f) + Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive d=/=e=/=f=/=g=/=h=/=i=/=j=/=k and Ptop(n) = binomial(n+3,4).
MATHEMATICA
Union[Total/@Subsets[Binomial[Range[4, 15], 4], {8}]] (* Harvey P. Dale, Mar 11 2012 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 05 2005
EXTENSIONS
Extended by Ray Chandler, Mar 05 2005
STATUS
approved