A104397 - OEIS

%I #18 Dec 14 2015 05:52:43

%S 462,582,666,722,747,757,777,787,791,831,887,922,942,951,952,956,967,

%T 1007,1042,1051,1062,1072,1076,1091,1107,1126,1142,1146,1156,1160,

%U 1162,1171,1172,1176,1182,1202,1212,1216,1227,1237,1247,1251,1253,1262,1267

%N Sums of 7 distinct positive pentatope numbers (A000332).

%C Pentatope number Ptop(n) = binomial(n+3,4) = n*(n+1)*(n+2)*(n+3)/24.

%C 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.

%D Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.

%H Hyun Kwang Kim, <a href="http://dx.doi.org/10.1090/S0002-9939-02-06710-2">On Regular Polytope Numbers</a>, Proc. Amer. Math. Soc., 131 (2003), 65-75.

%H J. V. Post, <a href="http://www.magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentatopeNumber.html">Pentatope Number</a>.

%F a(n) = Ptop(e) + Ptop(f) + Ptop(g) + Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive e=/=f=/=g=/=h=/=i=/=j=/=k and Ptop(n) = binomial(n+3,4).

%Y Cf. A000332, A100009, A102857, A104392, A104393, A104394, A104395, A104396.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 05 2005

%E Extended by _Ray Chandler_, Mar 05 2005