A104393 Sums of 3 distinct positive pentatope numbers (A000332).

21, 41, 51, 55, 76, 86, 90, 106, 110, 120, 132, 142, 146, 162, 166, 176, 197, 201, 211, 216, 226, 230, 231, 246, 250, 260, 281, 285, 295, 315, 336, 337, 341, 346, 350, 351, 366, 370, 371, 380, 401, 405, 406, 415, 435, 457, 461, 471, 491, 501

Offset

0,1

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=0..49.

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(i) + Ptop(j) + Ptop(k) for some positive i=/=j=/=k and Ptop(n) = binomial(n+3,4).

Mathematica

Total/@Subsets[Table[Binomial[n+3, 4], {n, 10}], {3}]//Sort (* Harvey P. Dale, Feb 14 2018 *)

Crossrefs

Cf. A000332, A100009, A102857, A104392.

Sequence in context: A084856 A070666 A320775 * A261522 A215145 A154576

Adjacent sequences: A104390 A104391 A104392 * A104394 A104395 A104396

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved