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 A141844 #43 Sep 08 2022 08:45:35
%S A141844 1,6,27,113,458,1839,7365,29470,117891,471577,1886322,7545303,
%T A141844 30181229,120724934,482899755,1931599041,7726396186,30905584767,
%U A141844 123622339093,494489356398,1977957425619,7911829702505,31647318810050,126589275240231,506357100960957
%N A141844 Expansion of (1+x)*(1+x^2)/((1-x)^2*(1+x+x^2)*(1-4*x)).
%C A141844 Old name was: a(n) = 4*a(n-1) + A042968(n), with a(0) = 1, where A042968 = "not divisible by 4": (1, 2, 3, 5, 6, 7, 9, 10, 11, ...). After the correction of a(13) the definition could be simplified. - _N. J. A. Sloane_, Aug 23 2018
%H A141844 Michael De Vlieger, <a href="/A141844/b141844.txt">Table of n, a(n) for n = 0..1660</a>
%H A141844 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -4, 1, -5, 4).
%F A141844 a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3) - 5*a(n-4) + 4*a(n-5) for n>4. - _Colin Barker_, Jun 26 2017
%e A141844 a(3) = 4*a(2) + A042968(3) = 4*27 + 5 = 113.
%e A141844 a(13) = 4*a(12) + A042968(13) = 4*30181229 + 18 = 120724934.
%t A141844 CoefficientList[Series[(1 + x) (1 + x^2) / ((1 - x)^2 (1 + x + x^2) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 28 2017 *)
%t A141844 Nest[Append[#, Block[{k = #[[-1, -1]] + 1}, While[Mod[k, 4] == 0, k++]; {4 #[[-1, 1]] + k, k}]] &, {{1, 1}}, 24][[All, 1]] (* _Michael De Vlieger_, Jun 30 2018 *)
%t A141844 LinearRecurrence[{5, -4, 1, -5, 4}, {1, 6, 27, 113, 458}, 25] (* _Robert G. Wilson v_, Jul 28 2018 *)
%o A141844 (PARI) Vec((1 + x)*(1 + x^2) / ((1 - x)^2*(1 - 4*x)*(1 + x + x^2)) + O(x^30)) \\ _Colin Barker_, Jun 26 2017
%o A141844 (Magma) I:=[1,6,27,113,458]; [n le 5 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3)-5*Self(n-4)+4*Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Jun 28 2017, Jul 28 2018
%Y A141844 Cf. A042968.
%K A141844 nonn
%O A141844 0,2
%A A141844 _Gary W. Adamson_, Jul 11 2008
%E A141844 Corrected by _Charlie Neder_, Jun 22 2018
%E A141844 Edited by _N. J. A. Sloane_, Aug 23 2018, merging old entry A288571 with this one.