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 A262734 #29 Mar 04 2025 07:36:59
%S A262734 1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,
%T A262734 3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,
%U A262734 5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,8,9
%N A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).
%C A262734 Decimal expansion of 111111112/900000009.
%C A262734 For n which lies in the interval [16*(k-1), 8*(2*k-1)], where k>0 -> pattern {1, 2, 3, 4, 5, 6, 7, 8, 9}; for n which lies in the interval [16*k - 7, 16*k - 1], where k>0 -> pattern {8, 7, 6, 5, 4, 3, 2}.
%H A262734 Colin Barker, <a href="/A262734/b262734.txt">Table of n, a(n) for n = 0..1000</a>
%H A262734 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,-1,1).
%F A262734 -1 + a(16*(k - 1)) = -2 + a(8*k + 3*(-1)^k - 4) = -3 + a(2*(4*k + (-1)^k - 2)) = -4 + a(8*k + (-1)^k - 4) = -5 + a(4*(2*k - 1)) = -6 + a(8*k - (-1)^k - 4) = -7 + a(-2*(-4*k + (-1)^k + 2)) = -8 + a(8*k - 3*(-1)^k - 4) = -9 + a(8*(2*k - 11)) = 0, for k>0.
%F A262734 a(0) = 1, a(n) = a(n+1) - 1, for 16*(k - 1) <= n < 8*(2*k - 1), and a(n) = a(n + 1) + 1, for 8*(2*k - 1) <= n < 16*k, where k>0.
%F A262734 From _Colin Barker_, Sep 29 2015: (Start)
%F A262734 a(n) = a(n-1) - a(n-8) + a(n-9) for n>8.
%F A262734 G.f.: -(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)*(x^8+1)). (End)
%t A262734 LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9}, 120] (* _Vincenzo Librandi_, Sep 29 2015 *)
%o A262734 (PARI) Vec(-(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)*(x^8+1)) + O(x^100)) \\ _Colin Barker_, Sep 29 2015
%o A262734 (Magma) &cat[[1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2]: n in [0..10]]; // _Vincenzo Librandi_, Sep 29 2015
%o A262734 (PARI) 111111112/900000009. \\ _Altug Alkan_, Sep 29 2015
%o A262734 (PARI) vector(200, n, default(realprecision, n+2); floor(111111112/900000009*10^n)%10) \\ _Altug Alkan_, Nov 12 2015
%Y A262734 Cf. A158289, A177274, A010889, A138531, A181975, A199264, A068073, A028356.
%K A262734 nonn,easy
%O A262734 0,2
%A A262734 _Ilya Gutkovskiy_, Sep 29 2015