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A194237 a(n) = [Sum_{k=1..n} (3k/8)], where [ ]=floor, ( )=fractional part.

%I A194237 #21 Dec 12 2024 11:29:18
%S A194237 0,1,1,1,2,2,3,3,3,4,4,5,6,6,7,7,7,8,8,8,9,9,10,10,10,11,11,12,13,13,
%T A194237 14,14,14,15,15,15,16,16,17,17,17,18,18,19,20,20,21,21,21,22,22,22,23,
%U A194237 23,24,24,24,25,25,26,27,27,28,28,28,29,29,29,30,30,31,31,31,32
%N A194237 a(n) = [Sum_{k=1..n} (3k/8)], where [ ]=floor, ( )=fractional part.
%H A194237 G. C. Greubel, <a href="/A194237/b194237.txt">Table of n, a(n) for n = 1..5000</a>
%H A194237 <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 A194237 From _Chai Wah Wu_, Jun 10 2020: (Start)
%F A194237 a(n) = a(n-1) + a(n-16) - a(n-17) for n > 17.
%F A194237 G.f.: x*(x^14 + x^12 + x^11 + x^9 + x^6 + x^4 + x)/(x^17 - x^16 - x + 1). (End)
%t A194237 r = 3/8;
%t A194237 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194237 Table[a[n], {n, 1, 90}]    (* A194237 *)
%t A194237 s[n_] := Sum[a[k], {k, 1, n}]
%t A194237 Table[s[n], {n, 1, 100}]   (* A194238 *)
%Y A194237 Cf. A194238.
%K A194237 nonn
%O A194237 1,5
%A A194237 _Clark Kimberling_, Aug 20 2011