A168098 a(n) = number of natural numbers m such that n - 8 <= m <= n + 8.

8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17

Offset

0,1

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

Table of n, a(n) for n=0..57.

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

Formula

a(n) = 8 + n for 0 <= n <= 8, a(n) = 17 for n >= 9.

G.f.: (8 - 7*x - x^10)/(1 - x)^2. - G. C. Greubel, Jul 12 2016

Mathematica

CoefficientList[Series[(8 - 7*x - x^10)/(1 - x)^2, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)

Crossrefs

Cf. A000027.

Sequence in context: A217292 A004164 A004449 * A020722 A046037 A089017

Adjacent sequences: A168095 A168096 A168097 * A168099 A168100 A168101

Keyword

nonn,less

Author

Jaroslav Krizek, Nov 18 2009

Status

approved