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

Author

Carmine Suriano, Jan 12 2011

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A000045, A000290, A179334.