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 A299914 #26 Mar 11 2018 09:50:57 %S A299914 0,1,1,6,9,42,69,306,513,2250,3789,16578,27945,122202,206037,900882, %T A299914 1518993,6641514,11198493,48963042,82558521,360969210,608644773, %U A299914 2661166386,4487100705,19618866954,33080169069,144635805954,243876313161,1066295850138,1797924789621 %N A299914 a(n) = a(n-1) + 3*a(n-2) if n even, or 2*a(n-1) + 4*a(n-2) if n odd, starting with 0, 1. %D A299914 Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31. %H A299914 Colin Barker, <a href="/A299914/b299914.txt">Table of n, a(n) for n = 0..1000</a> %H A299914 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,9,0,-12) %F A299914 G.f.: -x*(3*x^2-x-1)/(12*x^4-9*x^2+1). - _Alois P. Heinz_, Mar 10 2018 %F A299914 a(n) = 9*a(n-2) - 12*a(n-4) for n>3. - _Colin Barker_, Mar 11 2018 %p A299914 a:= n-> (<<0|1>, <-12|9>>^iquo(n, 2, 'r'). <<r, 5*r+1>>)[1, 1]: %p A299914 seq(a(n), n=0..35); # _Alois P. Heinz_, Mar 10 2018 %t A299914 Fold[Append[#1, Inner[Times, Boole[OddQ@ #2] + {1, 3}, {#1[[-1]], #1[[-2]]}, Plus]] &, {0, 1}, Range[2, 30]] (* or *) %t A299914 CoefficientList[Series[-x (3 x^2 - x - 1)/(12 x^4 - 9 x^2 + 1), {x, 0, 30}], x] (* _Michael De Vlieger_, Mar 10 2018 *) %o A299914 (PARI) concat(0, Vec(x*(1 + x - 3*x^2) / (1 - 9*x^2 + 12*x^4) + O(x^30))) \\ _Colin Barker_, Mar 11 2018 %Y A299914 Bisections give A299915, A299916. %Y A299914 Cf. A299913. %K A299914 nonn,easy %O A299914 0,4 %A A299914 _N. J. A. Sloane_, Mar 10 2018 %E A299914 More terms from _Altug Alkan_, Mar 10 2018