A168095 - OEIS

%I #13 Jun 29 2023 12:50:03

%S 5,6,7,8,9,10,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,

%T 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,

%U 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11

%N a(n) = number of natural numbers m such that n - 5 <= m <= n + 5.

%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) = 5 + n for 0 <= n <= 5, a(n) = 11 for n >= 6.

%F G.f.: (5 - 4*x - x^7)/(1-x)^2. - _G. C. Greubel_, Jul 12 2016

%t CoefficientList[Series[(5 - 4*x - x^7)/(1 - x)^2, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 12 2016 *)

%Y Cf. A000027.

%K nonn,less

%O 0,1

%A _Jaroslav Krizek_, Nov 18 2009