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 A133684 #18 May 27 2024 14:41:57 %S A133684 0,1,1,0,1,2,3,2,5,6,11,10,21,22,43,42,85,86,171,170,341,342,683,682, %T A133684 1365,1366,2731,2730,5461,5462,10923,10922,21845,21846,43691,43690, %U A133684 87381,87382,174763,174762,349525,349526,699051,699050,1398101,1398102,2796203,2796202 %N A133684 a(2n) = A001045(n); a(1)=1; a(2n+1) = 2*A001045(n-1) for n >= 1. %H A133684 Andrew Howroyd, <a href="/A133684/b133684.txt">Table of n, a(n) for n = 0..1000</a> %H A133684 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,2). %F A133684 a(4*n) + a(4*n+1) = a(4*n+2). %F A133684 a(n) + a(n+2) = 2^floor(n/2) = A016116(n). %F A133684 O.g.f.: x - x^2*(1 + 2*x^3)/((2*x^2-1)*(x^2+1)) . - _R. J. Mathar_, Feb 23 2008 %F A133684 a(n+1) = 2*A135318(n) - A135318(n+1). - _Paul Curtz_, May 27 2024 %o A133684 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 2,0,1,0]^n*[0;1;1;0])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016 %Y A133684 Cf. A001045, A016116, A133730 (first differences). %K A133684 nonn,easy %O A133684 0,6 %A A133684 _Paul Curtz_, Jan 04 2008 %E A133684 Terms a(24) and beyond from _Andrew Howroyd_, Feb 02 2020