A115315 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.

0, 0, 1, 2, 4, 6, 11, 17, 28, 46, 75, 121, 197, 319, 516, 836, 1353, 2189, 3542, 5731, 9273, 15004, 24278, 39283, 63562, 102845, 166408, 269253, 435661, 704915, 1140577, 1845492, 2986070, 4831563, 7817633, 12649197, 20466831, 33116028

Offset

0,4

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

L:= GoldenRatio/Sqrt[5]; Phi:= GoldenRatio;
f[n_]:= Floor[L^3*{Phi^(3*n-2), Phi^(3*n-1), Phi^(3*n-2) +Phi^(3*n-1)}];
Flatten[Table[f[n], {n, 1, 25}]]

Crossrefs

Cf. A000045.

Sequence in context: A222047 A210520 A018144 * A004698 A014217 A034297

Adjacent sequences: A115312 A115313 A115314 * A115316 A115317 A115318

Keyword

nonn,less

Author

Roger L. Bagula, Mar 06 2006

Extensions

Edited by G. C. Greubel, May 15 2019

Status

approved