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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified August 21 13:36 EDT 2017. Contains 290890 sequences.