cp's OEIS Frontend

A194165 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r = (1+sqrt(5))/2, the golden ratio.

%I A194165 #12 Nov 12 2017 03:03:50
%S A194165 0,0,1,2,2,2,3,4,4,4,5,6,6,6,7,8,8,8,9,9,10,11,11,12,12,12,13,13,14,
%T A194165 15,15,16,16,16,17,17,18,18,19,19,20,21,21,21,22,23,23,23,24,24,25,25,
%U A194165 26,26,27,28,28,29,29,30,30,31,31,32,32,33,33,33,34,34,35,36,36
%N A194165 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r = (1+sqrt(5))/2, the golden ratio.
%H A194165 G. C. Greubel, <a href="/A194165/b194165.txt">Table of n, a(n) for n = 1..5000</a>
%t A194165 r = GoldenRatio;
%t A194165 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194165 Table[a[n], {n, 1, 90}]  (* A194165 *)
%t A194165 s[n_] := Sum[a[k], {k, 1, n}]
%t A194165 Table[s[n], {n, 1, 100}] (* A194166 *)
%o A194165 (PARI) a(n) = floor(sum(k=1, n, frac((1+sqrt(5))*k/2))); \\ _Michel Marcus_, Nov 12 2017
%Y A194165 Cf. A194166.
%K A194165 nonn
%O A194165 1,4
%A A194165 _Clark Kimberling_, Aug 18 2011