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
Examples
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.)
Programs
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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
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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 *)
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
Extensions
More terms from Robert G. Wilson v, May 30 2017
Comments