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 A129345 #14 Apr 29 2025 19:15:27
%S A129345 2,9,12,53,70,309,408,1801,2378,10497,13860,61181,80782,356589,470832,
%T A129345 2078353,2744210,12113529,15994428,70602821,93222358,411503397,
%U A129345 543339720,2398417561,3166815962,13979001969,18457556052,81475594253,107578520350,474874563549
%N A129345 a(2n) = A001542(n+1), a(2n+1) = A038761(n+1); a Pellian-related sequence.
%C A129345 Summation of -a(n) and A129346 returns twice Pell numbers A000129 (apart from signs; starting from 2nd term of A000129).
%H A129345 Colin Barker, <a href="/A129345/b129345.txt">Table of n, a(n) for n = 0..1000</a>
%H A129345 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1).
%F A129345 G.f.: (2+9*x-x^3)/((x^2+2*x-1)*(x^2-2*x-1)).
%F A129345 From _Colin Barker_, May 26 2016: (Start)
%F A129345 a(n) = ((-1-sqrt(2))^(1+n)-(-1+sqrt(2))^(1+n)+(1-sqrt(2))^n*(-4+3*sqrt(2))+(1+sqrt(2))^n*(4+3*sqrt(2)))/(2*sqrt(2)).
%F A129345 a(n) = 6*a(n-2)-a(n-4) for n>3.
%F A129345 (End)
%t A129345 CoefficientList[Series[(2 + 9 x - x^3)/((x^2 + 2 x - 1) (x^2 - 2 x - 1)), {x, 0, 29}], x] (* _Michael De Vlieger_, May 26 2016 *)
%t A129345 LinearRecurrence[{0,6,0,-1},{2,9,12,53},30] (* _Harvey P. Dale_, Apr 29 2025 *)
%o A129345 (PARI) Vec((2+9*x-x^3)/((x^2+2*x-1)*(x^2-2*x-1)) + O(x^40)) \\ _Colin Barker_, May 26 2016
%Y A129345 Cf. A129346, A000129, A001542, A038761.
%K A129345 easy,nonn
%O A129345 0,1
%A A129345 _Creighton Dement_, Apr 10 2007