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A168099 a(n) = number of natural numbers m such that n - 9 <= m <= n + 9.

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%I A168099 #12 Jun 29 2023 12:53:57
%S A168099 9,10,11,12,13,14,15,16,17,18,19,19,19,19,19,19,19,19,19,19,19,19,19,
%T A168099 19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,
%U A168099 19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19
%N A168099 a(n) = number of natural numbers m such that n - 9 <= m <= n + 9.
%C A168099 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). a(n) = 9 + n for 0 <= n <= 9, a(n) = 19 for n >= 10.
%H A168099 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A168099 G.f.: (9 - 8*x - x^11)/(1 - x)^2. - _G. C. Greubel_, Jul 12 2016
%t A168099 CoefficientList[Series[(9 - 8*x - x^11)/(1 - x)^2, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 12 2016 *)
%K A168099 nonn
%O A168099 0,1
%A A168099 _Jaroslav Krizek_, Nov 18 2009