A168092 a(n) = number of natural numbers m such that n - 2 <= m <= n + 2.

2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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) = (2 + n) for 0 <= n <= 2, a(n) = 5 for n >= 3.

Links

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

Crossrefs

Cf. A158411. - Jaume Oliver Lafont, Nov 29 2009

Formula

G.f.: (2+x+x^2+x^3)/(1-x) = 1/(1-x)+(1-x^4)/(1-x)^2. - Jaume Oliver Lafont, Nov 29 2009