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

0,1

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..89.

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

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

Mathematica

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

Crossrefs

Cf. A000027.

Sequence in context: A178053 A090925 A143836 * A367063 A089166 A178052

Adjacent sequences: A168091 A168092 A168093 * A168095 A168096 A168097

Keyword

nonn,less

Author

Jaroslav Krizek, Nov 18 2009

Status

approved