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 A111662 #24 Mar 26 2024 11:36:47
%S A111662 0,0,1,2,4,9,18,36,72,144,288,576,1152,2304,4610,9220,18440,36882,
%T A111662 73764,147528,295056,590112,1180224,2360450,4720900,9441800,18883606,
%U A111662 37767212,75534424,151068852,302137704,604275408,1208550818,2417101636
%N A111662 Expansion of x^2*(1-x)*(x^2+x+1)*(x^6+x^3+1)/((2*x-1)*(2*x^9-x^6+x^3-1)).
%C A111662 Initial terms factored: [0,0,1,2,(2)^2,(3)^2,(2) (3)^2,(2)^2 (3)^2,(2)^3 (3)^2,(2)^4 (3)^2,(2)^5 (3)^2,(2)^6 (3)^2,(2)^7 (3)^2,(2)^8 (3)^2,(2) (5) (461),(2)^2 (5) (461),(2)^3 (5) (461),(2) (3)^3 (683),(2)^2 (3)^3 (683),(2)^3 (3)^3 (683),(2)^4 (3)^3 (683),(2)^5 (3)^3 (683),(2)^6 (3)^3 (683),(2) (5)^2 (17) (2777),(2)^2 (5)^2 (17) (2777),(2)^3 (5)^2 (17) (2777),(2) (7) (19) (70991),(2)^2 (7) (19) (70991),(2)^3 (7) (19) (70991),(2)^2 (3)^2 (11) (381487)]
%C A111662 Note that for each 3 terms in a row the sequence doubles: a(3*n+1) = 2*a(3*n) = 4*a(3*n-1). _Andrew Howroyd_, Mar 09 2024
%C A111662 Floretion Algebra Multiplication Program, FAMP Code: 2ibaseksumseq[.5'i + .5i' + .5'ii' + .5'jj' + .5'kk' + .5e], sumtype: sum[(Y[0], Y[1], Y[2]),mod(3)
%H A111662 G. C. Greubel, <a href="/A111662/b111662.txt">Table of n, a(n) for n = 0..1000</a>
%H A111662 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,-2,0,-1,2,0,2,-4).
%F A111662 a(n) = 2*a(n-1) + a(n-3) - 2*a(n-4) - a(n-6) + 2*a(n-7) + 2*a(n-9) - 4*a(n-10) for n>11. - _Colin Barker_, May 11 2019
%t A111662 CoefficientList[Series[x^2*(1 - x)*(x^2 + x + 1)*(x^6 + x^3 + 1)/((2*x - 1)*(2*x^9 - x^6 + x^3 - 1)), {x, 0, 50}], x] (* _G. C. Greubel_,Jun 09 2017 *)
%t A111662 LinearRecurrence[{2,0,1,-2,0,-1,2,0,2,-4},{0,0,1,2,4,9,18,36,72,144,288,576},40] (* _Harvey P. Dale_, Mar 26 2024 *)
%o A111662 (PARI) Vec(x^2*(1-x)*(x^2+x+1)*(x^6+x^3+1)/((2*x-1)*(2*x^9-x^6+x^3-1))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A111662 Cf. A111663.
%K A111662 nonn,easy
%O A111662 0,4
%A A111662 _Creighton Dement_, Aug 14 2005