A190993 Square excess of Fibonacci numbers.

0, 0, 0, 1, 2, 1, 4, 4, 5, 9, 6, 8, 0, 8, 16, 34, 26, 76, 84, 85, 41, 130, 22, 96, 143, 496, 289, 169, 842, 140, 296, 669, 2684, 1449, 343, 4096, 7583, 592, 665, 11682, 699, 20452, 2872, 22037, 6477, 21826, 17999, 93009, 46080, 31240, 121681, 8638, 317523

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Maple

a:= n-> (f-> f-floor(sqrt(f))^2)((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=0..52);  # Alois P. Heinz, Oct 26 2022

Mathematica

A000045=Fibonacci[Range[0, 100]]; Table[A000045[[n]]-Floor[Sqrt[A000045[[n]]]]^2, {n, Length[A000045]}]

Prog

(PARI) a(n) = my(f=fibonacci(n)); f - sqrtint(f)^2; \\ Michel Marcus, Nov 11 2015
(Magma) [Fibonacci(n) - Floor(Sqrt(Fibonacci(n)))^2: n in [0..100]]; // G. C. Greubel, Oct 26 2022
(SageMath) [fibonacci(n) - isqrt(fibonacci(n))^2 for n in range(101)] # G. C. Greubel, Oct 26 2022

Crossrefs

Cf. A000045, A190992, A216223.

Sequence in context: A019963 A165417 A193631 * A326147 A351168 A196082

Adjacent sequences: A190990 A190991 A190992 * A190994 A190995 A190996

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 02 2011

Extensions

a(0) prepended by Alois P. Heinz, Nov 11 2015

Status

approved