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A194222
a(n) = floor(Sum_{k=1..n} frac(k/5)), where frac() = fractional part.
2
0, 0, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 10, 10, 11, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 16, 16, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 20, 20, 21, 22, 22, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 26, 26, 27, 28, 28, 28, 28, 29, 30
OFFSET
1,4
FORMULA
From Chai Wah Wu, Jun 10 2020: (Start)
a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.
G.f.: x^3*(x + 1)/((x-1)^2*(1+x+x^2+x^3+x^4)). (End)
a(n) = floor((n+1)/5) + floor((n+2)/5). - Ridouane Oudra, Dec 14 2021
a(n) = A002266(n+1)+A002266(n+2). - R. J. Mathar, Nov 21 2023
MAPLE
seq(floor((n+1)/5)+floor((n+2)/5), n=1..80); # Ridouane Oudra, Dec 14 2021
MATHEMATICA
r = 1/5;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194222 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A118015 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 0, 1, 2, 2, 2}, 80] (* Harvey P. Dale, Jun 06 2024 *)
CROSSREFS
Cf. A118015.
Sequence in context: A261221 A080352 A301426 * A025779 A085003 A119026
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 19 2011
STATUS
approved