A104395 Sums of 5 distinct positive pentatope numbers (A000332).

126, 182, 217, 237, 247, 251, 266, 301, 321, 331, 335, 357, 377, 386, 387, 391, 412, 421, 422, 426, 441, 442, 446, 451, 455, 456, 477, 497, 507, 511, 532, 542, 546, 551, 561, 562, 566, 576, 581, 586, 591, 595, 606, 616, 620, 626, 630, 642, 646, 650

Offset

1,1

Comments

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

Robert Israel, Table of n, a(n) for n = 1..10000

Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.

Eric Weisstein's World of Mathematics, Pentatope Number.

Formula

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

Maple

N:= 1000: # for terms <= N
ptop:= n -> n*(n+1)*(n+2)*(n+3)/24:
P:= 1:
for i from 1 while ptop(i) < N do
  P:= P * (1 + x*y^ptop(i))
od:
sort(map(degree, convert(convert(series(coeff(P, x, 5), y, N+1), polynom), list)));
# Robert Israel, Nov 20 2023

Crossrefs

Cf. A000332, A100009, A102857, A104392, A104393, A104394.

Sequence in context: A009944 A203566 A320292 * A267331 A267739 A290203

Adjacent sequences: A104392 A104393 A104394 * A104396 A104397 A104398

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 05 2005

Extensions

Extended by Ray Chandler, Mar 05 2005

Status

approved