A287733 First differences of A069497.

6, 30, 30, 12, 42, 90, 66, 24, 78, 150, 102, 36, 114, 210, 138, 48, 150, 270, 174, 60, 186, 330, 210, 72, 222, 390, 246, 84, 258, 450, 282, 96, 294, 510, 318, 108, 330, 570, 354, 120, 366, 630, 390, 132, 402, 690, 426, 144, 438, 750, 462, 156, 474, 810, 498, 168, 510, 870, 534

Offset

1,1

Comments

First differences of the subsequence of triangular numbers that are divisible by 6.

By definition, these numbers are themselves divisible by 6.

Links

Table of n, a(n) for n=1..59.

Formula

G.f.: 6*(x^2+4*x+1)*(x^2-x+1)/((x-1)^2*(x^2+1)^2). - Robert Israel, May 30 2017

Example

The first triangular number divisible by 6 is 6, and the second triangular number divisible by 6 is 36.  Therefore a(2) = 36 - 6 = 30. (The zeroth triangular number divisible by 6 is taken to be 0.)

Maple

S:= [seq(seq((12*i+j)*(12*i+j+1)/2, j=[0, 3, 8, 11]), i=0..50)]:
S[2..-1]-S[1..-2]; # Robert Israel, May 30 2017

Mathematica

Differences@ Select[Array[# (# + 1)/2 &, 180, 0], Mod[#, 6] == 0 &] (* Robert G. Wilson v, May 30 2017 *)
Differences[Select[Accumulate[Range[0, 209]], Divisible[#, 6] &]] (* Alonso del Arte, May 31 2017 *)

Crossrefs

Cf. A069497, A108782, A154293.

Sequence in context: A375287 A351773 A123624 * A066197 A078638 A068510

Adjacent sequences: A287730 A287731 A287732 * A287734 A287735 A287736

Keyword

nonn,look

Author

Greg Huber, May 30 2017

Extensions

More terms from Robert G. Wilson v, May 30 2017

Status

approved