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 A140096 #18 Jul 18 2017 12:05:04
%S A140096 0,1,1,1,1,1,1,-1,-7,-23,-59,-139,-311,-677,-1443,-3031,-6295,-12967,
%T A140096 -26543,-54073,-109743,-222071,-448323,-903411,-1817767,-3653245,
%U A140096 -7335147,-14716663,-29508351,-59138095,-118472607
%N A140096 a(n) = A000045(n) - A113405(n).
%C A140096 Because the inverse binomial transform of A000045 and A113405 is individually the same as the original sequence up to a sign flip of each second term, the same is true for their difference here. (The inverse binomial transform is a linear transform.)
%C A140096 The sequence and its higher order differences in subsequent rows has zeros on the main diagonal:
%C A140096 0, 1, 1, 1, 1, 1, 1, -1, -7,-23, -59, -139, -311, -677, -1443, -3031
%C A140096 1, 0, 0, 0, 0, 0, -2, -6,-16,-36, -80, -172, -366, -766, -1588, -3264
%C A140096 -1, 0, 0, 0, 0,-2, -4,-10,-20,-44, -92, -194, -400, -822, -1676
%C A140096 1, 0, 0, 0,-2,-2, -6,-10,-24,-48,-102, -206, -422, -854, -1732
%C A140096 -1, 0, 0,-2, 0,-4, -4,-14,-24,-54,-104, -216, -432, -878, -1764
%C A140096 1, 0,-2, 2,-4, 0,-10,-10,-30,-50,-112, -216, -446, -886, -1790,
%C A140096 -1,-2, 4,-6, 4,-10, 0,-20,-20,-62,-104, -230, -440, -904, -1792
%H A140096 G. C. Greubel, <a href="/A140096/b140096.txt">Table of n, a(n) for n = 0..1000</a>
%H A140096 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,3,-1,-2).
%F A140096 a(n)= +3*a(n-1) -a(n-2) -3*a(n-3) +3*a(n-4) -a(n-5) -2*a(n-6).
%F A140096 G.f.: -x*(-1+2*x+x^2-2*x^3+x^4) / ( (2*x-1)*(1+x)*(x^2-x+1)*(x^2+x-1) ).
%F A140096 a(n+1)-2*a(n) = -A141325(n-2), n>2.
%t A140096 CoefficientList[Series[-x*(-1 + 2*x + x^2 - 2*x^3 + x^4)/((2*x - 1)*(1 + x)*(x^2 - x + 1)*(x^2 + x - 1)), {x, 0, 50}], x] (* _G. C. Greubel_, Jul 17 2017 *)
%o A140096 (PARI) x='x+O('x^50); concat([0], Vec(-x*(-1+2*x+x^2-2*x^3+x^4)/( (2*x-1)*(1+x)*(x^2-x+1)*(x^2+x-1) ))) \\ _G. C. Greubel_, Jul 17 2017
%Y A140096 Cf. A140428, A140413.
%K A140096 sign,easy,less
%O A140096 0,9
%A A140096 _Paul Curtz_, Jun 21 2008