A129965 Triangular numbers that are the difference of nonnegative cubes.

0, 1, 91, 4095, 5886, 7875, 8128, 8911, 9045, 17955, 21736, 23653, 47278, 93961, 115921, 130816, 184528, 259560, 379756, 488566, 575128, 658378, 758296, 810901, 873181, 885115, 1060696, 1155960, 1358776, 1385280, 1997001, 2616328, 2685403

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..439 (terms <= 10^12)

Example

A000217(13) = Sum_{k=1..13} k = 91 = 216 - 125 = 6^3 - 5^3, so 91 is in the sequence. - Peter Munn, Dec 05 2022

Maple

M:= 10^7: # for terms <= M
S:= {0}:
for x from 1 while 3*x^2 - 3*x + 1 < M do
   if x^3 < M then Y:= 0 else Y:= ceil(x^3-M) fi;
  S:= S union select(t -> issqr(1+8*t), {seq(x^3 - y^3, y = Y .. x-1)});
od:
sort(convert(S, list)); # Robert Israel, Dec 05 2023

Mathematica

With[{n = 5000}, Intersection[(#1*((#1 + 1)/2) & ) /@ Range[0, n], Flatten[Outer[ #1^3 - #2^3 &, Range[n], Range[0, n - 1]]]]]

Crossrefs

Intersection of A000217 and A152043.

Cf. A038596, A129966, A185253.

Sequence in context: A169937 A047697 A096054 * A017807 A017754 A283383

Adjacent sequences: A129962 A129963 A129964 * A129966 A129967 A129968

Keyword

nonn

Author

Peter Pein (petsie(AT)dordos.net), Jun 13 2007, Jun 14 2007

Status

approved