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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(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..45.

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(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).

CROSSREFS

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

Sequence in context: A267396 A258962 A267332 * A108749 A267740 A254468

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

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Last modified December 9 23:16 EST 2016. Contains 278993 sequences.