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 A080456 #33 Mar 03 2024 11:41:17
%S A080456 2,2,6,10,14,18,18,22,26,30,30,34,38,42,42,46,50,54,54,58,62,66,66,70,
%T A080456 74,78,78,82,86,90,90,94,98,102,102,106,110,114,114,118,122,126,126,
%U A080456 130,134,138,138,142,146,150,150,154,158,162,162,166,170,174,174
%N A080456 a(1) = a(2) = 2; for n > 2, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.
%C A080456 First differences are 4-periodic.
%H A080456 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A080456 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%H A080456 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1).
%F A080456 From _Chai Wah Wu_, Jul 17 2016: (Start)
%F A080456 a(n) = a(n-1) + a(n-4) - a(n-5) for n > 6.
%F A080456 G.f.: -2*(-1 - 2*x^2 - 2*x^3 - x^4 - 2*x^5 + 2*x^6)/((-1 + x)^2*(1 + x + x^2 + x^3)). (End)
%t A080456 Join[{2}, LinearRecurrence[{1, 0, 0, 1, -1}, {6, 10, 14, 18, 18}, 60]] (* _Jean-François Alcover_, Sep 02 2018 *)
%t A080456 CoefficientList[Series[-2*(-1 - 2 x^2 - 2 x^3 - x^4 - 2 x^5 + 2 x^6)/((-1 + x)^2 (1 + x +x^2 + x^3)), {x, 0, 60}],x] (* _Stefano Spezia_, Sep 02 2018 *)
%Y A080456 Cf. A080455, A080457, A080458, A080036, A080037.
%K A080456 nonn
%O A080456 1,1
%A A080456 _N. J. A. Sloane_, Mar 20 2003
%E A080456 a(1) = 2 prepended by _Stefano Spezia_, Sep 04 2018