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

Author

Eli Jaffe, Oct 24 2015

Keywords

• nonn
• easy

Examples

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

Crossrefs

Cf. A000045, A048760, A061287.

Programs

Mathematica

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

PARI

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

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