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a(n) = number of natural numbers m such that n - 6 <= m <= n + 6.
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%I #15 Jun 29 2023 12:51:04

%S 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 13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,

%U 13,13,13,13,13,13,13,13

%N a(n) = number of natural numbers m such that n - 6 <= m <= n + 6.

%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).

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

%F a(n) = 6 + n for 0 <= n <= 6, a(n) = 13 for n >= 7.

%F G.f.: (6 - 5*x - x^8)/(1-x)^2. - _G. C. Greubel_, Jul 12 2016

%t CoefficientList[Series[(6 - 5*x - x^8)/(1 - x)^2, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 12 2016 *)

%t PadRight[{6,7,8,9,10,11,12},120,{13}] (* _Harvey P. Dale_, May 24 2022 *)

%Y Cf. A000027.

%K nonn,less

%O 0,1

%A _Jaroslav Krizek_, Nov 18 2009