

A104392


Sums of 2 distinct positive pentatope numbers (A000332).


8



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
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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: SpringerVerlag, pp. 5557, 1996.


LINKS

Table of n, a(n) for n=0..49.
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(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: A217186 A101239 A242331 * A037001 A118139 A087446
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



