A104392 Sums of 2 distinct positive pentatope numbers (A000332).

6, 16, 20, 36, 40, 50, 71, 75, 85, 105, 127, 131, 141, 161, 196, 211, 215, 225, 245, 280, 331, 335, 336, 345, 365, 400, 456, 496, 500, 510, 530, 540, 565, 621, 705, 716, 720, 730, 750, 785, 825, 841, 925, 1002, 1006, 1016, 1036, 1045, 1071, 1127

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

Mathematica

nn=15; Select[Union[Total/@Subsets[Binomial[Range[4, nn], 4], {2}]], #<Binomial[nn, 4]+1&]  (* Harvey P. Dale, Mar 13 2011 *)

Crossrefs

Cf. A000332, A100009, A102856.

Sequence in context: A101239 A242331 A335226 * A291746 A037001 A118139

Adjacent sequences: A104389 A104390 A104391 * A104393 A104394 A104395

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved