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%I #21 May 31 2017 16:55:44
%S 6,30,30,12,42,90,66,24,78,150,102,36,114,210,138,48,150,270,174,60,
%T 186,330,210,72,222,390,246,84,258,450,282,96,294,510,318,108,330,570,
%U 354,120,366,630,390,132,402,690,426,144,438,750,462,156,474,810,498,168,510,870,534
%N First differences of A069497.
%C First differences of the subsequence of triangular numbers that are divisible by 6.
%C By definition, these numbers are themselves divisible by 6.
%F G.f.: 6*(x^2+4*x+1)*(x^2-x+1)/((x-1)^2*(x^2+1)^2). - _Robert Israel_, May 30 2017
%e 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 zeroeth triangular number divisible by 6 is taken to be 0.)
%p S:= [seq(seq((12*i+j)*(12*i+j+1)/2, j=[0,3,8,11]), i=0..50)]:
%p S[2..-1]-S[1..-2]; # _Robert Israel_, May 30 2017
%t Differences@ Select[Array[# (# + 1)/2 &, 180, 0], Mod[#, 6] == 0 &] (* _Robert G. Wilson v_, May 30 2017 *)
%t Differences[Select[Accumulate[Range[0, 209]], Divisible[#, 6] &]] (* _Alonso del Arte_, May 31 2017 *)
%Y Cf. A069497, A108782, A154293.
%K nonn,look
%O 1,1
%A _Greg Huber_, May 30 2017
%E More terms from _Robert G. Wilson v_, May 30 2017
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