A179459 Squares that are a sum of two Fibonacci numbers plus the square of a Fibonacci number.

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 169, 225, 289, 441, 676, 729, 784, 1156, 1444, 1600, 2601, 3025, 4624, 7921, 12544, 20736, 23409, 27556, 31684, 47524, 54289, 139129, 142129, 171396, 217156, 372100, 974169, 1488400, 2550409, 6677056, 10201636

Offset

1,1

Comments

The squares of A000045 (A007598) are basically a subsequence because they can be expressed as Fibonacci(k+3)^2 = Fibonacci(2k)+Fibonacci(2k+4)+Fibonacci(k-1)^2 or Fibonacci(k+2)^2 = Fibonacci(2k)+Fibonacci(2k+1)+Fibonacci(k)^2 or Fibonacci(2k+3)^2 = Fibonacci(4k)+Fibonacci(4k+4)+Fibonacci(2k-1)^2.

Links

Table of n, a(n) for n=1..41.

Example

a(5)=36=6*6=3+8+25=Fib(4)+Fib(6)+Fib(5)^2.

Crossrefs

Cf. A000045, A000290, A179334.

Sequence in context: A144913 A018885 A025741 * A325148 A325149 A326707

Adjacent sequences: A179456 A179457 A179458 * A179460 A179461 A179462

Keyword

nonn

Author

Carmine Suriano, Jan 12 2011

Status

approved