

A194223


a(n) = [sum{(k/6) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.


3



0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 25, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 30, 30, 30, 30
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OFFSET

1,5


LINKS



FORMULA

a(n) = a(n1) + a(n12)  a(n13) for n > 13.
G.f.: x*(x^10 + x^9 + x^7 + x^4 + x^2)/(x^13  x^12  x + 1). (End)


MATHEMATICA

r = 1/6;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194223 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194224 *)


PROG

(PARI) for(n=1, 50, print1(floor(sum(k=1, n, frac(k/6))), ", ")) \\ G. C. Greubel, Oct 29 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



