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 A354789 #25 Jul 25 2024 19:08:48
%S A354789 2,5,11,17,29,41,65,89,137,185,281,377,569,761,1145,1529,2297,3065,
%T A354789 4601,6137,9209,12281,18425,24569,36857,49145,73721,98297,147449,
%U A354789 196601,294905,393209,589817,786425,1179641,1572857,2359289,3145721,4718585,6291449,9437177,12582905,18874361,25165817,37748729,50331641,75497465
%N A354789 a(2*n) = 9*2^n - 7, a(2*n+1) = 3*2^(n+2) - 7.
%H A354789 Paolo Xausa, <a href="/A354789/b354789.txt">Table of n, a(n) for n = 0..1000</a>
%H A354789 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2).
%F A354789 G.f.: (2 + 3*x + 2*x^2)/((1 - x)*(1 - 2*x^2)). - _Stefano Spezia_, Feb 05 2023
%F A354789 E.g.f.: - 7*cosh(x) + 9*cosh(sqrt(2)*x) - 7*sinh(x) + 6*sqrt(2)*sinh(sqrt(2)*x). - _Stefano Spezia_, Jul 25 2024
%t A354789 LinearRecurrence[{1,2,-2},{2,5,11},100] (* _Paolo Xausa_, Oct 17 2023 *)
%t A354789 CoefficientList[Series[(2+3x+2x^2)/((1-x)(1-2x^2)),{x,0,50}],x] (* _Harvey P. Dale_, Jun 07 2024 *)
%Y A354789 The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283.
%K A354789 nonn,easy
%O A354789 0,1
%A A354789 _N. J. A. Sloane_, Jul 14 2022