A104398 Sums of 8 distinct positive pentatope numbers (A000332).

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

Table of n, a(n) for n=1..42.

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(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 *)

Crossrefs

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

Sequence in context: A263010 A351670 A282547 * A186057 A027817 A104680

Adjacent sequences: A104395 A104396 A104397 * A104399 A104400 A104401

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved