A263727 Largest square number less than or equal to the n-th Fibonacci number.

0, 1, 1, 1, 1, 4, 4, 9, 16, 25, 49, 81, 144, 225, 361, 576, 961, 1521, 2500, 4096, 6724, 10816, 17689, 28561, 46225, 74529, 121104, 196249, 316969, 514089, 831744, 1345600, 2175625, 3523129, 5702544, 9223369, 14922769, 24157225, 39087504, 63234304, 102333456

Offset

0,6

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = floor(sqrt(Fibonacci(n)))^2.

a(n) = A061287(n)^2. - Michel Marcus, Oct 25 2015

a(n) = A048760(A000045(n)). - Michel Marcus, Nov 11 2015

Example

For a(8), Fibonacci(8) = 21, the largest square under 21 is 16, so a(8) = 16.

Mathematica

Floor[Sqrt[Fibonacci[Range[40]]]]^2 (* Alonso del Arte, Oct 24 2015 *)

Prog

(PARI) a(n) = sqrtint(fibonacci(n))^2; \\ Michel Marcus, Oct 25 2015

Crossrefs

Cf. A000045, A048760, A061287.

Sequence in context: A226096 A071567 A304990 * A133037 A061886 A059815

Adjacent sequences: A263724 A263725 A263726 * A263728 A263729 A263730

Keyword

nonn,easy

Author

Eli Jaffe, Oct 24 2015

Status

approved