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
FORMULA
a(n) = 6 + n for 0 <= n <= 6, a(n) = 13 for n >= 7.
G.f.: (6 - 5*x - x^8)/(1-x)^2. - G. C. Greubel, Jul 12 2016
MATHEMATICA
CoefficientList[Series[(6 - 5*x - x^8)/(1 - x)^2, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)
PadRight[{6, 7, 8, 9, 10, 11, 12}, 120, {13}] (* Harvey P. Dale, May 24 2022 *)
CROSSREFS
KEYWORD
nonn,less
AUTHOR
Jaroslav Krizek, Nov 18 2009
STATUS
approved