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 A228577 #55 Sep 08 2022 08:46:05
%S A228577 0,1,0,2,2,3,6,7,12,17,24,36,50,72,102,143,202,282,394,549,762,1057,
%T A228577 1462,2019,2784,3832,5268,7232,9916,13581,18580,25394,34674,47303,
%U A228577 64478,87819,119520,162549,220920,300060,407302,552552,749186,1015259,1375134
%N A228577 The number of 1-length gaps in all possible covers of n-length line by 2-length segments.
%C A228577 2-gaps must be filled, so, for example, xxoo doesn't count for n=4. - _Jon Perry_, Nov 18 2014
%D A228577 A. G. Shannon, P. G. Anderson and A. F. Horadam, Properties of Cordonnier, Perrin and Van der Laan numbers, International Journal of Mathematical Education in Science and Technology, Volume 37:7 (2006), 825-831. See Eqn. (3.13). - _N. J. A. Sloane_, Jan 11 2022
%H A228577 D. Birmajer, J. Gil and M. Weiner, <a href="http://arxiv.org/abs/1405.7727">Linear recurrence sequences and their convolutions via Bell polynomials</a>, arXiv:1405.7727 [math.CO], 2014 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Gil/gil3.html">J. Int. Seq. 18 (2015) # 15.1.2</a>.
%H A228577 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-2,-1).
%F A228577 For n>1, a(n) = n * A228361(n) - 2 * A228364(n).
%F A228577 G.f.: x/(x^3 + x^2 - 1)^2, convolution of A182097 by itself.
%F A228577 a(n) = 2*a(n-2) +2*a(n-3) -a(n-4) -2*a(n-5) -a(n-6) for n>5.
%F A228577 (n-1)*a(n) - (n+1)*a(n-2) - (n+2)*a(n-3) = 0 for n>2. - _Michael D. Weiner_, Nov 18 2014
%e A228577 For n=6 we have xxoxxo, oxxxxo and oxxoxx, so a(6) = number of o's = 6. - _Jon Perry_, Nov 18 2014
%p A228577 A228577 := proc(n) coeftayl(x/(x^3+x^2-1)^2, x=0, n); end proc: seq(A228577(n), n=0..50); # _Wesley Ivan Hurt_, Nov 17 2014
%t A228577 CoefficientList[Series[x/(x^3 + x^2 - 1)^2, {x, 0, 100}], x]
%o A228577 (Magma) I:=[0,1,0,2,2,3]; [n le 6 select I[n] else 2*Self(n-2)+2*Self(n-3)-Self(n-4)-2*Self(n-5)-Self(n-6): n in [1..50]]; // _Vincenzo Librandi_, Nov 18 2014
%Y A228577 Cf. A228361, A228364.
%K A228577 nonn,easy
%O A228577 0,4
%A A228577 _Philipp O. Tsvetkov_, Aug 26 2013