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 A340849 #33 Feb 16 2024 14:32:35
%S A340849 0,1,3,5,9,15,27,49,93,179,351,693,1377,2743,5475,10937,21861,43707,
%T A340849 87399,174781,349545,699071,1398123,2796225,5592429,11184835,22369647,
%U A340849 44739269,89478513,178956999,357913971,715827913
%N A340849 a(n) = A001045(n) + A052928(n).
%C A340849 a(2*n) is divisible by 3.
%C A340849 a(3*n+2) is divisible by 3.
%C A340849 a(n) is the minimum number of moves to solve a Towers of Hanoi puzzle with 4 pegs and n disks where a disk cannot move away from the destination peg (or symmetrically, a disk cannot return to the initial peg). - _Woosuk Kwak_, Jan 25 2024
%H A340849 Woosuk Kwak, <a href="https://puzzling.stackexchange.com/q/125230/71652">1+3 Towers of Hanoi</a>, Puzzling Stack Exchange.
%H A340849 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%F A340849 a(n+1) - 2*a(n) = -A109613(n-2), for a(0)=0, a(1)=1. a(n) + a(n+1) = A100314(n).
%F A340849 a(n+1) - a(n) = A128209(n) for n >= 0.
%F A340849 a(n+2) = 1 + 2*A086445(n). - _Hugo Pfoertner_, Jan 24 2021
%F A340849 From _Woosuk Kwak_, Jan 25 2024: (Start)
%F A340849 a(n) = n + floor(2^n/3).
%F A340849 a(n) = n + A000975(n-1) for n >= 1. (End)
%t A340849 LinearRecurrence[{3, -1, -3, 2}, {0, 1, 3, 5}, 32] (* _Robert P. P. McKone_, Jan 28 2021 *)
%Y A340849 Cf. A001045, A052928, A100314, A109613, A128209.
%K A340849 nonn
%O A340849 0,3
%A A340849 _Paul Curtz_, Jan 24 2021