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A194235 a(n) = [Sum_{k=1..n} (k/8)], where [ ]=floor, ( )=fractional part.

%I A194235 #22 Dec 12 2024 11:23:36
%S A194235 0,0,0,1,1,2,3,3,3,3,4,4,5,6,7,7,7,7,7,8,8,9,10,10,10,10,11,11,12,13,
%T A194235 14,14,14,14,14,15,15,16,17,17,17,17,18,18,19,20,21,21,21,21,21,22,22,
%U A194235 23,24,24,24,24,25,25,26,27,28,28,28,28,28,29,29,30,31,31,31,31
%N A194235 a(n) = [Sum_{k=1..n} (k/8)], where [ ]=floor, ( )=fractional part.
%H A194235 G. C. Greubel, <a href="/A194235/b194235.txt">Table of n, a(n) for n = 1..5000</a>
%H A194235 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F A194235 From _Chai Wah Wu_, Jun 10 2020: (Start)
%F A194235 a(n) = a(n-1) + a(n-16) - a(n-17) for n > 17.
%F A194235 G.f.: x*(x^14 + x^13 + x^12 + x^10 + x^6 + x^5 + x^3)/(x^17 - x^16 - x + 1). (End)
%t A194235 r = 1/8;
%t A194235 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194235 Table[a[n], {n, 1, 90}]    (* A194235 *)
%t A194235 s[n_] := Sum[a[k], {k, 1, n}]
%t A194235 Table[s[n], {n, 1, 100}]   (* A194236 *)
%o A194235 (PARI) a(n) = floor(sum(k=1, n, frac(k/8))); \\ _Michel Marcus_, Nov 03 2017
%Y A194235 Cf. A194236.
%K A194235 nonn
%O A194235 1,6
%A A194235 _Clark Kimberling_, Aug 20 2011