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a(n) = number of natural numbers m such that n - 10 <= m <= n + 10.
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%I #16 Jun 29 2023 12:55:17

%S 10,11,12,13,14,15,16,17,18,19,20,21,21,21,21,21,21,21,21,21,21,21,21,

%T 21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,

%U 21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21

%N a(n) = number of natural numbers m such that n - 10 <= m <= n + 10.

%C 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) = 10 + n for 0 <= n <= 10, a(n) = 21 for n >= 11.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F G.f.: (10 - 9*x - x^12)/(1 - x)^2. - _G. C. Greubel_, Jul 12 2016

%t CoefficientList[Series[(10 - 9*x - x^12)/(1 - x)^2, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 12 2016 *)

%t Table[Count[Range[n-10,n+10],_?Positive],{n,0,80}] (* or *) PadRight[ {10,11,12,13,14,15,16,17,18,19,20},120,{21}] (* _Harvey P. Dale_, Jan 09 2019 *)

%K nonn

%O 0,1

%A _Jaroslav Krizek_, Nov 18 2009