This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A287733 #24 Apr 29 2024 10:52:48 %S A287733 6,30,30,12,42,90,66,24,78,150,102,36,114,210,138,48,150,270,174,60, %T A287733 186,330,210,72,222,390,246,84,258,450,282,96,294,510,318,108,330,570, %U A287733 354,120,366,630,390,132,402,690,426,144,438,750,462,156,474,810,498,168,510,870,534 %N A287733 First differences of A069497. %C A287733 First differences of the subsequence of triangular numbers that are divisible by 6. %C A287733 By definition, these numbers are themselves divisible by 6. %F A287733 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 A287733 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.) %p A287733 S:= [seq(seq((12*i+j)*(12*i+j+1)/2, j=[0,3,8,11]), i=0..50)]: %p A287733 S[2..-1]-S[1..-2]; # _Robert Israel_, May 30 2017 %t A287733 Differences@ Select[Array[# (# + 1)/2 &, 180, 0], Mod[#, 6] == 0 &] (* _Robert G. Wilson v_, May 30 2017 *) %t A287733 Differences[Select[Accumulate[Range[0, 209]], Divisible[#, 6] &]] (* _Alonso del Arte_, May 31 2017 *) %Y A287733 Cf. A069497, A108782, A154293. %K A287733 nonn,look %O A287733 1,1 %A A287733 _Greg Huber_, May 30 2017 %E A287733 More terms from _Robert G. Wilson v_, May 30 2017