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 A226122 #34 Jun 13 2015 00:54:40
%S A226122 1,2,1,3,6,3,5,10,5,7,14,7,9,18,9,11,22,11,13,26,13,15,30,15,17,34,17,
%T A226122 19,38,19,21,42,21,23,46,23,25,50,25,27,54,27,29,58,29,31,62,31,33,66,
%U A226122 33,35,70,35,37,74,37,39,78,39
%N A226122 Expansion of (1+2*x+x^2+x^3+2*x^4+x^5)/(1-2*x^3+x^6).
%C A226122 A226023 (starting from A226023(-2)=0) and successive differences:
%C A226122 0, -1, 0, 2, 3, 6, 12, 15, 20, 30,...
%C A226122 -1, 1, 2, 1, 3, 6, 3, 5, 10, 5,... = a(n-1)
%C A226122 2, 1, -1, 2, 3, -3, 2, 5, -5, 2,...
%C A226122 -1, -2, 3, 1, -6, 5, 3, -10, 7, 5,...
%C A226122 -1, 5, -2, -7, 11, -2, -13, 17, -2, -19,...
%C A226122 6, -7, -5, 18, -13, -11, 30, -19, -17, 42,...
%C A226122 -13, 2, 23, -31, 2, 41, -49, 2, 59, 67,...
%C A226122 15, 21, -54, 33, 39, -90, 51, 57, -126, 69,... multiples of 3
%C A226122 6, -75, 87, 6, -129, 141, 6, -183, 195, 6,... multiples of 3
%C A226122 -81, 162, -81, -135, 270, -135, -189, 378, -189, -243,... multiples of 27
%C A226122 The last line is -27*a(n+3)*A131561(n+1).
%C A226122 The recurrences in the Formula field hold for the array.
%H A226122 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A226122 a(n) = A130823(n-1) * A131534(n).
%F A226122 a(n) = A226023(n) - A226023(n-1) with A226023(-1)=-1.
%F A226122 a(n) = 3*a(n-3) -3*a(n-6) +a(n-9) = a(n-1) +2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7). [_Ralf Stephan_]
%F A226122 From _Bruno Berselli_, May 29 2013: (Start)
%F A226122 G.f.: (1+x)^3*(1-x+x^2)/((1-x)^2*(1+x+x^2)^2).
%F A226122 a(n) = 2*a(n-3)-a(n-6).
%F A226122 a(3n)*a(3n-1)-a(3n-2) = A016754(n-1), n>0. (End)
%e A226122 Given A130823 = 1,1,1,3,3,3,5,5,5,7,7,7,... and A131534 = 1,2,1,1,2,1,1,2,1,1,2,1,..., then a(0)=1*1=1, a(1)=1*2=2, a(2)=1*1=1, a(3)=3*1=3, a(4)=3*2=6, etc.
%e A226122 Given A226023(n) from A226023(-1)=-1, then a(0)=0-(-1)=1, a(1)=2-0=2, a(2)=3-2=1, a(3)=6-3=3, a(4)=12-6=6, etc.
%t A226122 repeat=20; Table[{1, 2, 1}, {repeat}]*(2*Range[repeat]-1) // Flatten
%t A226122 (* or *) Table[Floor[(2*n+1)/3]*Floor[(2*n+5)/3], {n, -1, 59}] // Differences (* _Jean-François Alcover_, May 29 2013 *)
%Y A226122 Cf. A005408, A016754, A130823, A131534, A226023.
%K A226122 nonn,easy
%O A226122 0,2
%A A226122 _Paul Curtz_, May 27 2013