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 A174191 #24 Dec 18 2023 12:20:52
%S A174191 1,2,3,6,13,30,71,170,409,986,2379,5742,13861,33462,80783,195026,
%T A174191 470833,1136690,2744211,6625110,15994429,38613966,93222359,225058682,
%U A174191 543339721,1311738122,3166815963,7645370046,18457556053,44560482150,107578520351
%N A174191 Expansion of (1+x)*(2*x-1)/((1-x)*(x^2+2*x-1)).
%C A174191 Pisano period lengths: 1, 2, 8, 4, 12, 8, 6, 8, 24, 12, 24, 8, 28, 6, 24, 16, 16, 24, 40, 12,.. (is this A175181?) - _R. J. Mathar_, Aug 10 2012
%H A174191 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-1).
%F A174191 a(n) = 2*a(n-1) + a(n-2) - 2, with a(0)=1, a(1)=2.
%F A174191 From _R. J. Mathar_, Mar 17 2010: (Start)
%F A174191 a(n) = A052937(n-1), n > 0.
%F A174191 a(n) = 3*a(n-1) - a(n-2) - a(n-3). (End)
%e A174191 a(2) = 2*a(1) + a(0) - 2 = 2*2 + 1 - 2 = 3
%e A174191 a(3) = 2*a(2) + a(1) - 2 = 2*3 + 2 - 2 = 6.
%t A174191 LinearRecurrence[{3, -1, -1}, {1, 2, 3}, 31] (* _Robert P. P. McKone_, Apr 03 2022 *)
%Y A174191 Cf. A174192, A001333 (first differences).
%K A174191 nonn
%O A174191 0,2
%A A174191 _Clark Kimberling_, Mar 11 2010