A115315 - OEIS

%I #12 May 15 2019 20:32:53

%S 0,0,1,2,4,6,11,17,28,46,75,121,197,319,516,836,1353,2189,3542,5731,

%T 9273,15004,24278,39283,63562,102845,166408,269253,435661,704915,

%U 1140577,1845492,2986070,4831563,7817633,12649197,20466831,33116028

%N a(n) = floor(L^3*{phi^(3*n-2), phi^(3*n-1), phi^(3*n-2) + phi^(3*n-1)}) where L = (1 + sqrt(5))/(2*sqrt(5)) and phi = (1 + sqrt(5))/2.

%C a(n) is the greatest multiple of L^3*phi^(3*n-2), L^3*phi^(3*n-1), and L^3*(phi^(3*n-2) + phi^(3*n-1)), where L = (1+sqrt(5))/(2*sqrt(5)) and phi = (1+sqrt(5))/2. - _G. C. Greubel_, May 15 2019

%H G. C. Greubel, <a href="/A115315/b115315.txt">Table of n, a(n) for n = 0..1000</a>

%F Empirical g.f.: x^2*(x^8-2*x^6+x^5+2*x^4-x^3-x^2+1) / ((x-1)*(x+1)*(x^2+x-1)*(x^4-x^3+x^2-x+1)*(x^8-x^6+x^4-x^2+1)). - _Colin Barker_, Mar 15 2013

%t L:= GoldenRatio/Sqrt[5]; Phi:= GoldenRatio;

%t f[n_]:= Floor[L^3*{Phi^(3*n-2), Phi^(3*n-1), Phi^(3*n-2) +Phi^(3*n-1)}];

%t Flatten[Table[f[n], {n, 1, 25}]]

%Y Cf. A000045.

%K nonn,less

%O 0,4

%A _Roger L. Bagula_, Mar 06 2006

%E Edited by _G. C. Greubel_, May 15 2019