A168094 a(n) = number of natural numbers m such that n - 4 <= m <= n + 4.

4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Author

Jaroslav Krizek, Nov 18 2009

Keywords

• nonn
• less

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).

Links

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

Crossrefs

Cf. A000027.

Programs

Mathematica

CoefficientList[Series[(4 - 3*x - x^6)/(1 - x)^2, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)

Formula

a(n) = 4 + n for 0 <= n <= 4, a(n) = 9 for n >= 4.

G.f.: (4 - 3*x - x^6)/(1 - x)^2. - G. C. Greubel, Jul 12 2016