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%I #12 Jun 10 2020 22:45:31
%S 0,0,1,1,1,2,3,3,3,3,4,4,4,5,6,6,6,6,7,7,7,8,9,9,9,9,10,10,10,11,12,
%T 12,12,12,13,13,13,14,15,15,15,15,16,16,16,17,18,18,18,18,19,19,19,20,
%U 21,21,21,21,22,22,22,23,24,24,24,24,25,25,25,26,27,27,27,27,28
%N [sum{(k/4) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.
%H G. C. Greubel, <a href="/A194220/b194220.txt">Table of n, a(n) for n = 1..5000</a>
%F From _Chai Wah Wu_, Jun 10 2020: (Start)
%F a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.
%F G.f.: x*(x^6 + x^5 + x^2)/(x^9 - x^8 - x + 1). (End)
%t r = 1/4;
%t a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t Table[a[n], {n, 1, 90}] (* A194220 *)
%t s[n_] := Sum[a[k], {k, 1, n}]
%t Table[s[n], {n, 1, 100}] (* A194221 *)
%Y Cf. A194221.
%K nonn
%O 1,6
%A _Clark Kimberling_, Aug 19 2011
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