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

Author

Vladimir Joseph Stephan Orlovsky, Jun 02 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A000045, A190992, A216223.

Programs

Magma

[Fibonacci(n) - Floor(Sqrt(Fibonacci(n)))^2: n in [0..100]]; // G. C. Greubel, Oct 26 2022

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]}]

PARI

a(n) = my(f=fibonacci(n)); f - sqrtint(f)^2; \\ Michel Marcus, Nov 11 2015

SageMath

[fibonacci(n) - isqrt(fibonacci(n))^2 for n in range(101)] # G. C. Greubel, Oct 26 2022

Extensions

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