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 A105423 #20 Mar 03 2024 14:11:51
%S A105423 1,0,3,3,9,15,31,57,108,199,366,666,1205,2166,3873,6891,12207,21537,
%T A105423 37859,66327,115842,201743,350412,607140,1049545,1810428,3116655,
%U A105423 5355219,9185349,15728547,26890375,45904773,78253896,133221079
%N A105423 Number of compositions of n+2 having exactly two parts equal to 1.
%C A105423 Column 2 of A105422.
%H A105423 Jia Huang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Huang/huang8.html">Partially Palindromic Compositions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 11.
%H A105423 J. J. Madden, <a href="http://arxiv.org/abs/1707.04351">A generating function for the distribution of runs in binary words</a>, arXiv:1707.04351 [math.CO], 2017. Theorem 1.1, r=1, k=2.
%H A105423 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -5, 0, 3, 1).
%F A105423 G.f.: (1-z)^3/(1-z-z^2)^3.
%F A105423 a(n) = (1/50) [(5n^2+21n+25)*Lucas(n) - (11n^2+30n+10)*Fibonacci(n) ]. - _Ralf Stephan_, Jun 01 2007
%e A105423 a(4)=9 because we have (1,1,4),(1,4,1),(4,1,1),(1,1,2,2),(1,2,1,2),(1,2,2,1),(2,1,1,2),(2,1,2,1) and (2,2,1,1).
%p A105423 G:=(1-z)^3/(1-z-z^2)^3: Gser:=series(G,z=0,42): 1,seq(coeff(Gser,z^n),n=1..40);
%t A105423 LinearRecurrence[{3, 0, -5, 0, 3, 1}, {1, 0, 3, 3, 9, 15}, 40] (* _Jean-François Alcover_, Jul 23 2018 *)
%Y A105423 Cf. A105422.
%K A105423 nonn,easy
%O A105423 0,3
%A A105423 _Emeric Deutsch_, Apr 07 2005