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 A168096 #15 Jun 29 2023 12:51:04 %S A168096 6,7,8,9,10,11,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13, %T A168096 13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13, %U A168096 13,13,13,13,13,13,13,13 %N A168096 a(n) = number of natural numbers m such that n - 6 <= m <= n + 6. %C A168096 Generalization: If a(n,k) = number of natural numbers m such that n - k <= m <= n + k (k >= 1) then a(n,k) = a(n-1,k) + 1 = n + k for 0 <= n <= k, a(n,k) = a(n-1,k) = 2k + 1 for n >= k + 1 (see, e.g., A158799). %H A168096 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A168096 a(n) = 6 + n for 0 <= n <= 6, a(n) = 13 for n >= 7. %F A168096 G.f.: (6 - 5*x - x^8)/(1-x)^2. - _G. C. Greubel_, Jul 12 2016 %t A168096 CoefficientList[Series[(6 - 5*x - x^8)/(1 - x)^2, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 12 2016 *) %t A168096 PadRight[{6,7,8,9,10,11,12},120,{13}] (* _Harvey P. Dale_, May 24 2022 *) %Y A168096 Cf. A000027. %K A168096 nonn,less %O A168096 0,1 %A A168096 _Jaroslav Krizek_, Nov 18 2009