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 A130668 #27 Sep 08 2022 08:45:30
%S A130668 0,0,1,-2,5,-11,23,-48,102,-220,476,-1024,2184,-4624,9744,-20480,
%T A130668 42976,-90048,188352,-393216,819328,-1704192,3539200,-7340032,
%U A130668 15203840,-31456256,65010688,-134217728,276826112,-570429440,1174409216
%N A130668 Diagonal of A129819.
%C A130668 This sequence is connected to A124072. To see this, change the sign of every negative term and consider the differences of every line. Hence for the second line, and following lines, the four terms form periodic sequences:
%C A130668 0 1 0 1 0
%C A130668 1 0 0 1 1
%C A130668 1 0 1 2 1
%C A130668 1 1 3 3 1
%C A130668 2 4 6 4 2
%C A130668 6 10 10 6 6
%C A130668 16 20 16 12 16
%C A130668 36 36 28 28 36
%C A130668 72 64 56 64 72
%C A130668 136 120 120 136 136
%C A130668 256 240 256 272 256.
%C A130668 The lines are connected as seen by the examples: (3rd line connected to 2nd, from right to left) 1+1=2, 1+0=1, 0+0=0, 0+1=1; (11th line connected to 10th) 136+136=272, 136+120=256, 120+120=240, 120+136=256.
%C A130668 The 4 columns are almost known (must the first line be suppressed?): A038503 (without the first 1), A000749 (without the first 0), A038505, A038504. Like the present sequence, every sequence of A124072 beginning with a negative number (-2, -11, ...) is a "twisted" sequence (see A129339 comments, A129961 and the present 4 columns). Periodic with period 2^n.
%C A130668 Inverse binomial transform of A129819. - _R. J. Mathar_, Feb 25 2009
%H A130668 G. C. Greubel, <a href="/A130668/b130668.txt">Table of n, a(n) for n = 0..1000</a>
%H A130668 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-14,-16,-8).
%F A130668 From _R. J. Mathar_, Feb 25 2009: (Start)
%F A130668 G.f.: x^2*(1+x)*(1 + 3*x + 4*x^2 + 3*x^3)/((1 + 2*x + 2*x^2)*(1+2*x)^2).
%F A130668 a(n) = ((-1)^n*A001787(n+1) - 4*A108520(n) + 4*A122803(n))/32, n > 2. (End)
%F A130668 a(n) = -6*a(n-1) - 14*a(n-2) - 16*a(n-3) - 8*a(n-4) for n >= 7. - _G. C. Greubel_, Mar 24 2019
%t A130668 gf = x^2*(1+x)*(1+3*x+4*x^2+3*x^3)/((1+2*x+2*x^2)*(1+2*x)^2); CoefficientList[Series[gf, {x, 0, 30}], x] (* _Jean-François Alcover_, Dec 16 2014, after _R. J. Mathar_ *)
%t A130668 Join[{0, 0, 1}, LinearRecurrence[{-6,-14,-16,-8}, {-2,5,-11,23}, 30]] (* _Jean-François Alcover_, Feb 15 2016 *)
%o A130668 (PARI) my(x='x+O('x^30)); concat([0,0], Vec(x^2*(1+x)*(1+3*x+4*x^2+3*x^3 )/((1+2*x +2*x^2)*(1+2*x)^2))) \\ _G. C. Greubel_, Mar 24 2019
%o A130668 (Magma) I:=[-2,5,-11,23]; [0,0,1] cat [n le 4 select I[n] else -6*Self(n-1) - 14*Self(n-2)-16*Self(n-3)-8*Self(n-4): n in [1..30]]; // _G. C. Greubel_, Mar 24 2019
%o A130668 (Sage) (x^2*(1+x)*(1+3*x+4*x^2+3*x^3)/((1+2*x+2*x^2)*(1+2*x)^2 )).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 24 2019
%o A130668 (GAP) a:=[-2,5,-11,23];; for n in [5..30] do a[n]:=-6*a[n-1]+-14*a[n-2] -16*a[n-3]-8*a[n-4]; od; Concatenation([0,0,1], a); # _G. C. Greubel_, Mar 24 2019
%K A130668 sign
%O A130668 0,4
%A A130668 _Paul Curtz_, Jun 27 2007
%E A130668 Extended by _R. J. Mathar_, Feb 25 2009