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 A010710 #89 Oct 29 2024 12:20:35
%S A010710 4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,
%T A010710 4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,
%U A010710 4,5,4,5,4,5,4,5,4,5,4,5,4
%N A010710 Period 2: repeat [4,5].
%C A010710 Continued fraction of 2 + 2*sqrt(30)/5 = A176215. - _R. J. Mathar_, Nov 21 2011
%C A010710 Decimal expansion of 5/11. - _Franklin T. Adams-Watters_, Jan 25 2019
%C A010710 Also, a(n) is the number of binary sequences of length n+3 avoiding the subsequences 000, 001, 011, 111. For example, when n=5 the a(5)=5 sequences of length 8 are 01010101, 10101010, 01010100, 11010101, 11010100. - _Miquel A. Fiol_, Dec 28 2023
%H A010710 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A010710 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A010710 G.f.: (4+5*x)/(1-x^2). - _Jaume Oliver Lafont_, Mar 20 2009
%F A010710 a(n) = floor(9*(n+1)/2) - floor(9*n/2). - _Hailey R. Olafson_, Jul 17 2014
%F A010710 a(n) = 4 + (n mod 2). - _Kritsada Moomuang_, Sep 06 2018
%F A010710 From _Wesley Ivan Hurt_, Apr 20 2024: (Start)
%F A010710 a(n+2) = a(n).
%F A010710 a(n+1) = a(n) + (-1)^n.
%F A010710 a(n) = (9-(-1)^n)/2. (End)
%t A010710 From _Stefano Spezia_, Sep 07 2018: (Start)
%t A010710 a[n_]:=-(1/2)*(-1)^n + 9/2; Array[a, 50, {0, 49}]
%t A010710 a[n_]:=Floor[9*(n+1)/2] - Floor[9*n/2]; Array[a, 50, {0, 49}]
%t A010710 a[n_]:= 4 + Mod[n,2]; Array[a, 50, {0, 49}]
%t A010710 LinearRecurrence[{0, 1}, {4, 5}, 50]
%t A010710 CoefficientList[Series[(4+5*x)/(1-x^2), {x, 0, 50}], x]
%t A010710 (End)
%o A010710 (PARI) a(n)=4+n%2 \\ _Jaume Oliver Lafont_, Mar 20 2009
%o A010710 (PARI) a(n) = my(v=[4, 5]); v[n%2+1] \\ _Felix Fröhlich_, Sep 06 2018
%o A010710 (PARI) Vec((4+5*x)/(1-x^2) + O(x^100)) \\ _Felix Fröhlich_, Sep 06 2018
%Y A010710 Cf. A176215.
%K A010710 nonn,easy
%O A010710 0,1
%A A010710 _N. J. A. Sloane_