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 A166517 #35 Feb 24 2023 04:29:36
%S A166517 2,1,5,4,8,7,11,10,14,13,17,16,20,19,23,22,26,25,29,28,32,31,35,34,38,
%T A166517 37,41,40,44,43,47,46,50,49,53,52,56,55,59,58,62,61,65,64,68,67,71,70,
%U A166517 74,73,77,76,80,79,83,82,86,85,89,88,92,91,95,94,98,97,101,100,104,103,107
%N A166517 a(n) = (3 + 5*(-1)^n + 6*n)/4.
%C A166517 A sequence defined by a(1)=1, a(n)=k*n-a(n-1), k a constant parameter, has recurrence a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). Its generating function is x*(1+2*(k-1)*x+(1-k)*x^2)/((1+x)*(1-x)^2). The closed form is a(n) = k*n/2+k/4+(-1)^n*(3*k/4-1). This applies with k=3 to this sequence here, and for example to sequences A165033, and A166519-A166525. - _R. J. Mathar_, Oct 17 2009
%C A166517 From _Paul Curtz_, Feb 20 2010: (Start)
%C A166517 Also: A001651, terms swapped by pairs.
%C A166517 a(n) mod 9 defines a period-6 sequence which is a permutation of A141425. (End)
%H A166517 Vincenzo Librandi, <a href="/A166517/b166517.txt">Table of n, a(n) for n = 0..1000</a>
%H A166517 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A166517 a(n) = 3*n - a(n-1).
%F A166517 From _Paul Curtz_, Feb 20 2010: (Start)
%F A166517 a(n+1)-a(n) = (-1)^(n+1)*A010685(n).
%F A166517 Second differences: |a(n+2)-2*a(n+1)+a(n)| = A010716(n).
%F A166517 a(2*n) + a(2*n+1) = A016945(n) = 6*n+3.
%F A166517 a(2*n) = A016945(n).
%F A166517 a(2*n+1) = A016777(n). (End)
%F A166517 G.f. ( 2-x+2*x^2 ) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Mar 08 2011
%F A166517 E.g.f.: (1/4)*exp(-x)*(5 + 3*exp(2*x) + 6*x*exp(2*x)). - _G. C. Greubel_, May 15 2016
%F A166517 Sum_{n>=0} (-1)^(n+1)/a(n) = Pi/(3*sqrt(3)) (A073010). - _Amiram Eldar_, Feb 24 2023
%t A166517 CoefficientList[Series[(2 x^2 - x + 2)/((1 + x) (x - 1)^2), {x, 0, 80}], x] (* _Harvey P. Dale_, Mar 25 2011 *)
%t A166517 Table[(3 + 5 (-1)^n + 6 n) / 4, {n, 0, 100}] (* _Vincenzo Librandi_, Sep 13 2013 *)
%o A166517 (Magma) [(3 +5*(-1)^n+6*n)/4: n in [0..80]]; // _Vincenzo Librandi_, Sep 13 2013
%Y A166517 Cf. A001651, A010685, A010716, A016777, A016945, A073010.
%K A166517 nonn,easy
%O A166517 0,1
%A A166517 _Vincenzo Librandi_, Oct 16 2009
%E A166517 a(0)=2 added by _Paul Curtz_, Feb 20 2010