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A190248 a(n) = [nu+nv+nw]-[nu]-[nv]-[nw], where u=(1+sqrt(5))/2, v=u^2, w=u^3, []=floor.

%I A190248 #34 Jan 05 2025 19:51:39
%S A190248 1,0,2,1,0,1,1,2,1,0,2,1,0,1,1,2,1,0,1,1,2,1,0,2,1,0,1,1,2,1,0,2,1,0,
%T A190248 1,0,2,1,0,1,1,2,1,0,2,1,0,1,1,2,1,0,2,1,2,1,0,2,1,0,1,1,2,1,0,2,1,0,
%U A190248 1,1,2,1,0,1,1,2,1,0,2,1,0,1,1,2,1,0,2,1,0,1,0,2,1,0,1,1,2,1,0,2,1,0,1,1,2,1,0,1
%N A190248 a(n) = [nu+nv+nw]-[nu]-[nv]-[nw], where u=(1+sqrt(5))/2, v=u^2, w=u^3, []=floor.
%C A190248 a(n) = A190440(n) - A078588(n). This follows from substituting w = 1+2u, v = 1+u, and taking 2n, n and n out of the floor functions. - _Michel Dekking_, Oct 21 2016
%H A190248 G. C. Greubel, <a href="/A190248/b190248.txt">Table of n, a(n) for n = 1..10000</a>
%H A190248 Burghard Herrmann, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/57-5/herrmann.pdf">How integer sequences find their way into areas outside pure mathematics</a>, The Fibonacci Quarterly (2019) Vol. 57, No. 5, 67-71.
%F A190248 a(n) = [2n+4nu]-[nu]-[n+nu]-[n+2nu], where u=(1+sqrt(5))/2. - _Michel Dekking_, Oct 21 2016
%t A190248 u = GoldenRatio; v = u^2; w=u^3;
%t A190248 f[n_] := Floor[n*u + n*v + n*w] - Floor[n*u] - Floor[n*v] - Floor[n*w]
%t A190248 t = Table[f[n], {n, 1, 120}] (* A190248 *)
%t A190248 Flatten[Position[t, 0]]      (* A190249 *)
%t A190248 Flatten[Position[t, 1]]      (* A190250 *)
%t A190248 Flatten[Position[t, 2]]      (* A190251 *)
%o A190248 (PARI) for(n=1,30, print1(floor(2*n*(2+sqrt(5))) - floor(n*(1+sqrt(5))/2) - floor(n*(3 + sqrt(5))/2) - floor(n*(2 + sqrt(5))), ", ")) \\ _G. C. Greubel_, Dec 26 2017
%o A190248 (Magma) [Floor(2*n*(2+Sqrt(5))) - Floor(n*(1+Sqrt(5))/2) - Floor(n*(3 + Sqrt(5))/2): n in [1..30]]; // _G. C. Greubel_, Dec 26 2017
%Y A190248 Cf. A190249, A190250, A190251.
%K A190248 nonn
%O A190248 1,3
%A A190248 _Clark Kimberling_, May 06 2011
%E A190248 Name corrected by _Michel Dekking_, Oct 21 2016