

A104397


Sums of 7 distinct positive pentatope numbers (A000332).


3



462, 582, 666, 722, 747, 757, 777, 787, 791, 831, 887, 922, 942, 951, 952, 956, 967, 1007, 1042, 1051, 1062, 1072, 1076, 1091, 1107, 1126, 1142, 1146, 1156, 1160, 1162, 1171, 1172, 1176, 1182, 1202, 1212, 1216, 1227, 1237, 1247, 1251, 1253, 1262, 1267
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Pentatope number Ptop(n) = binomial coefficient binomial(n,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: SpringerVerlag, pp. 5557, 1996.


LINKS

Table of n, a(n) for n=1..45.
Hyun Kwang Kim, On regular polytope numbers, Proc. Amer. Math. Soc. 131 (2003), 6575.
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
Eric Weisstein's World of Mathematics, Pentatope Number.


FORMULA

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 coefficient binomial(n, 4).


CROSSREFS

Cf. A000332, A100009, A102857, A104392, A104393, A104394, A104395, A104396.
Sequence in context: A101734 A059025 A094380 * A108749 A242321 A222342
Adjacent sequences: A104394 A104395 A104396 * A104398 A104399 A104400


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Mar 05 2005


EXTENSIONS

Extended by Ray Chandler Mar 05 2005


STATUS

approved



