A089988 Possible differences of n^2*(n+1)/2.

5, 12, 17, 22, 34, 35, 39, 51, 57, 69, 70, 74, 86, 92, 108, 117, 120, 121, 125, 145, 156, 162, 176, 178, 190, 195, 209, 210, 213, 247, 248, 262, 270, 279, 282, 287, 321, 330, 354, 365, 376, 386, 387, 399, 404, 424

Offset

1,1

Comments

Vaguely related to x^3+y^3=z^3, as x^3=2x.A000217(x) - x^2, e.g. 3^3=2.3.6 - 9 = 27.

Links

Table of n, a(n) for n=1..46.

Formula

n^2*(n+1)/2 - m^2*(m+1)/2 for all n>m

Example

5^2*(5+1)/2=25*3=75 and 3^2*(3+1)/2=9*2=18, so 75-18=57 is in the sequence

Prog

(PARI) { v=vector(300); c=0; for (i=1, 20, for (j=i, 20, v[c++ ]=tn(j)-tn(i))); v=vecsort(v); v }

Crossrefs

Cf. A000217, A002411 (pentagonal pyramidal numbers).

Sequence in context: A314284 A293034 A314285 * A314286 A314287 A135459

Adjacent sequences: A089985 A089986 A089987 * A089989 A089990 A089991

Keyword

nonn

Author

Jon Perry, Jan 14 2004

Status

approved