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 A077882 #12 Aug 09 2025 17:23:52
%S A077882 0,1,1,2,4,5,9,14,20,33,49,74,116,173,265,406,612,937,1425,2162,3300,
%T A077882 5013,7625,11614,17652,26865,40881,62170,94612,143933,218953,333158,
%U A077882 506820,771065,1173137,1784706,2715268,4130981,6284681,9561518,14546644,22130881,33669681
%N A077882 Expansion of x/((1-x)*(1-x^2-2*x^3)).
%C A077882 a(n+1) gives diagonal sums of Riordan array (1/(1-x),x*(1+2*x)) and partial sums of A052947. - _Paul Barry_, Jul 18 2005
%H A077882 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-2).
%F A077882 a(n) = a(n-1)+a(n-2)+a(n-3)-2*a(n-4). - _Roger L. Bagula_, Mar 25 2005
%F A077882 a(n+1) = Sum_{k=0..n} Sum_{j=0..floor(k/2)} C(j, k-2*j)*2^(k-2*j). - _Paul Barry_, Jul 18 2005
%t A077882 a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 2; a[n_Integer?Positive] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] - 2a[n - 4]; aa = Table[a[n], {n, 0, 42}] (* _Roger L. Bagula_, Mar 25 2005 *)
%t A077882 CoefficientList[Series[x/((1-x)(1-x^2-2x^3)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,1,-2},{0,1,1,2},50] (* _Harvey P. Dale_, Aug 17 2017 *)
%K A077882 nonn,easy
%O A077882 0,4
%A A077882 _N. J. A. Sloane_, Nov 17 2002
%E A077882 Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of _R. J. Mathar_