A168100 a(n) = number of natural numbers m such that n - 10 <= m <= n + 10.

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

Offset: 0

Author

Jaroslav Krizek, Nov 18 2009

Keywords

• nonn

Comments

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Programs

Mathematica

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

Formula

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