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 A192920 #22 Sep 08 2022 08:45:58
%S A192920 0,5,8,26,63,170,440,1157,3024,7922,20735,54290,142128,372101,974168,
%T A192920 2550410,6677055,17480762,45765224,119814917,313679520,821223650,
%U A192920 2149991423,5628750626,14736260448,38580030725,101003831720,264431464442
%N A192920 Coefficient of x in the reduction by (x^2 -> x+1) of the polynomial F(n+4)*x^n, where F=A000045 (Fibonacci sequence).
%C A192920 See A192872.
%H A192920 G. C. Greubel, <a href="/A192920/b192920.txt">Table of n, a(n) for n = 0..1000</a>
%H A192920 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F A192920 a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3).
%F A192920 a(n) = A192883(n+1).
%F A192920 G.f.: x*(5-2*x)/((1+x)*(1-3*x+x^2)). - _R. J. Mathar_, Aug 01 2011
%F A192920 a(n) = (A005248(n+2) - 7*(-1)^n)/5. - _R. J. Mathar_, Aug 01 2011
%F A192920 a(n) = Fibonacci(n+2)^2 - (-1)^n. - _G. C. Greubel_, Feb 06 2019
%F A192920 Sum_{n>=1} 1/a(n) = 7/18. - _Amiram Eldar_, Oct 05 2020
%t A192920 (* First program *)
%t A192920 q = x^2; s = x + 1; z = 28;
%t A192920 p[0, x_]:= 3; p[1, x_]:= 5 x;
%t A192920 p[n_, x_]:= p[n-1, x]*x + p[n-2, x]*x^2;
%t A192920 Table[Expand[p[n, x]], {n, 0, 7}]
%t A192920 reduce[{p1_, q_, s_, x_}]:= FixedPoint[(s PolynomialQuotient @@ #1 + PolynomialRemainder @@ #1 &)[{#1, q, x}] &, p1]
%t A192920 t = Table[reduce[{p[n, x], q, s, x}], {n, 0, z}];
%t A192920 u1 = Table[Coefficient[Part[t, n], x, 0], {n, 1, z}] (* A192919 *)
%t A192920 u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}] (* A192920 *)
%t A192920 (* Second program *)
%t A192920 LinearRecurrence[{2,2,-1}, {0,5,8}, 30] (* _G. C. Greubel_, Feb 06 2019 *)
%o A192920 (PARI) vector(30, n, n--; fibonacci(n+2)^2 -(-1)^n) \\ _G. C. Greubel_, Feb 06 2019, modified Jul 28 2019
%o A192920 (Magma) [Fibonacci(n+2)^2 -(-1)^n: n in [0..30]]; // _G. C. Greubel_, Feb 06 2019, modified Jul 28 2019
%o A192920 (Sage) [fibonacci(n+2)^2 -(-1)^n for n in (0..30)] # _G. C. Greubel_, Feb 06 2019, modified Jul 28 2019
%o A192920 (GAP) a:=[0,5,8];; for n in [4..30] do a[n]:=2*a[n-1]+2*a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Feb 06 2019
%Y A192920 Cf. A000045, A192232, A192744, A192872, A192883, A192919.
%K A192920 nonn
%O A192920 0,2
%A A192920 _Clark Kimberling_, Jul 12 2011