|
|
A172128
|
|
a(n) = floor(phi^n/n), where phi = golden ratio = (1+sqrt(5))/2.
|
|
3
|
|
|
1, 1, 1, 1, 2, 2, 4, 5, 8, 12, 18, 26, 40, 60, 90, 137, 210, 320, 492, 756, 1165, 1800, 2786, 4320, 6710, 10440, 16266, 25380, 39650, 62016, 97108, 152213, 238824, 375060, 589521, 927368, 1459960, 2300100
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
LINKS
|
|
|
FORMULA
|
a(n) = floor((1/n)*(Fibonacci(n)*phi + Fibonacci(n-1)), where phi = (1+sqrt(5))/2.
|
|
MATHEMATICA
|
Table[Floor[((1 + Sqrt[5])/2)^n/n], {n, 1, 50}]
Table[Floor[GoldenRatio^n/n], {n, 50}] (* Harvey P. Dale, Dec 12 2018 *)
|
|
PROG
|
(Magma) [Floor((Lucas(n) + Sqrt(5)*Fibonacci(n))/(2*n)): n in [1..50]]; // G. C. Greubel, Apr 17 2022
(SageMath) [floor(golden_ratio^n/n) for n in (1..50)] # G. C. Greubel, Apr 17 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|