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

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 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, 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, 19, 19, 19, 19, 19, 19, 19, 19, 19

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) = 9 + n for 0 <= n <= 9, a(n) = 19 for n >= 10.

Links

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

Programs

Mathematica

CoefficientList[Series[(9 - 8*x - x^11)/(1 - x)^2, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)

Formula

G.f.: (9 - 8*x - x^11)/(1 - x)^2. - G. C. Greubel, Jul 12 2016