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 A269226 #64 Oct 23 2018 06:21:53
%S A269226 3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,
%T A269226 9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,
%U A269226 6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3,3,9,6,6,9,3
%N A269226 Period 6: repeat [3, 9, 6, 6, 9, 3].
%C A269226 The palindromic sequence arising when the digital root of n alternates diagonally in opposite directions on a square grid. This is the sequence of 3-6-9 appearing every third column on a square grid when A010888 (digital root of n) alternates in both directions diagonally. Other columns are the digital root of 2^n: {1, 2, 4, 8, 7, 5}, or in its opposite direction 5^n: {5,7,8,4,2,1}. All diagonals parallel to the digital roots of n are also {1,2,3,4,5,6,7,8,9} or {9,8,7,6,5,4,3,2,1}.
%C A269226 See the link below for a visual illustration.
%C A269226 This sequence also arises when A180592 (digital root of 2n) is substituted for A010888.
%C A269226 Decimal expansion of 40070/10101. - _David A. Corneth_, Jul 12 2016
%H A269226 Peter M. Chema, <a href="/A269226/a269226_4.pdf">Illustration of initial terms</a>
%H A269226 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).
%F A269226 a(n+1) = digital root of 5^n - 2^n.
%F A269226 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) = a(n-6). - _Charles R Greathouse IV_, Jul 12 2016
%F A269226 a(n) = (12 - 3*cos(n*Pi/3) - 3*cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - 3*sqrt(3)*sin(2*n*Pi/3))/2. - _Wesley Ivan Hurt_, Oct 05 2018
%o A269226 (PARI) a(n)=[3, 3, 9, 6, 6, 9][n%6+1] \\ _Charles R Greathouse IV_, Jul 12 2016
%Y A269226 Cf. A010888, A180592.
%K A269226 nonn,base,easy
%O A269226 1,1
%A A269226 _Peter M. Chema_, Jul 11 2016