A182576 Number of 1's in the Zeckendorf representation of n^2.

0, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 4, 4, 4, 3, 3, 3, 4, 3, 4, 4, 3, 3, 3, 4, 5, 5, 6, 4, 5, 3, 3, 5, 3, 4, 3, 6, 4, 2, 4, 4, 5, 6, 6, 7, 3, 4, 6, 5, 4, 5, 5, 5, 5, 6, 3, 5, 7, 4, 5, 6, 4, 6, 4, 5, 6, 5, 6, 6, 6, 4, 6, 7, 7, 8, 5, 6, 7, 6, 6, 7, 4, 4, 6, 3

Offset

0,3

Comments

Also the minimum number of different Fibonacci numbers that sum up to n^2. - Carmine Suriano, Jul 03 2013

See A088060 for some comments related to the occurrence of 2's. - Peter Munn, Mar 22 2021

Links

Carmine Suriano, Table of n, a(n) for n = 0..1000

Example

a(11)=4 since 11^2 = 121 = 89 + 21 + 8 + 3 = fib(11) + fib(8) + fib(6) + fib(4). - Carmine Suriano, Jul 03 2013

Crossrefs

Cf. A007895, A020908, A020910, A025496-A025502, A088060, A182535, A182580.

Sequence in context: A263873 A263799 A299230 * A368869 A128330 A133801

Adjacent sequences: A182573 A182574 A182575 * A182577 A182578 A182579

Keyword

nonn

Author

Alex Ratushnyak, May 05 2012

Status

approved