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

Author

Jonathan Vos Post, Mar 05 2005

Keywords

• easy
• nonn

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

• 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.

Crossrefs

Cf. A000332, A100009, A102857, A104392.

Programs

Mathematica

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

Formula

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

Extensions

Extended by Ray Chandler, Mar 05 2005