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 A195013 #46 Feb 09 2024 12:40:08
%S A195013 2,3,4,6,6,9,8,12,10,15,12,18,14,21,16,24,18,27,20,30,22,33,24,36,26,
%T A195013 39,28,42,30,45,32,48,34,51,36,54,38,57,40,60,42,63,44,66,46,69,48,72,
%U A195013 50,75,52,78,54,81,56,84,58,87,60,90,62,93,64,96,66,99,68,102
%N A195013 Multiples of 2 and of 3 interleaved: a(2n-1) = 2n, a(2n) = 3n.
%C A195013 First differences of A195014.
%H A195013 Reinhard Zumkeller, <a href="/A195013/b195013.txt">Table of n, a(n) for n = 1..10000</a>
%H A195013 D. H. Bailey, J. M. Borwein, and J. S. Kimberley, <a href="https://www.davidhbailey.com/dhbtalks/dhb-mpfun-pphi.pdf">Discovery of large Poisson polynomials using a new arbitrary precision software package</a>, Slides, 2015.
%H A195013 D. H. Bailey, J. M. Borwein, and J. S. Kimberley, <a href="http://www.davidhbailey.com/dhbpapers/poisson-res.pdf">Computer discovery and analysis of large Poisson polynomials</a>, 2016.
%H A195013 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A195013 Pair(2*n, 3*n).
%F A195013 From _Bruno Berselli_, Sep 26 2011: (Start)
%F A195013 G.f.: x*(2+3*x)/(1-x^2)^2.
%F A195013 a(n) = (5*n+(n-2)*(-1)^n+2)/4.
%F A195013 a(n) = 2*a(n-2) - a(n-4) = a(n-2) + A010693(n-1).
%F A195013 a(n)+a(-n) = A010673(n).
%F A195013 a(n)-a(-n) = A106832(n). (End)
%t A195013 With[{r = Range[50]}, Riffle[2*r, 3*r]] (* or *)
%t A195013 LinearRecurrence[{0, 2, 0, -1}, {2, 3, 4, 6}, 100] (* _Paolo Xausa_, Feb 09 2024 *)
%o A195013 (Magma) &cat[[2*n,3*n]: n in [1..34]]; // _Bruno Berselli_, Sep 25 2011
%o A195013 (Haskell)
%o A195013 import Data.List (transpose)
%o A195013 a195013 n = a195013_list !! (n-1)
%o A195013 a195013_list = concat $ transpose [[2, 4 ..], [3, 6 ..]]
%o A195013 -- _Reinhard Zumkeller_, Apr 06 2015
%o A195013 (PARI) a(n)=(5*n+(n-2)*(-1)^n+2)/4 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A195013 Cf. A005843, A008585, A195014, A195019.
%Y A195013 Cf. A111712 (partial sums of this sequence prepended with 1).
%K A195013 nonn,easy
%O A195013 1,1
%A A195013 _Omar E. Pol_, Sep 09 2011