A179334 -id:A179334 - cp's OEIS frontend

A111378 Squares that are equal to the sum of two Fibonacci numbers.

0, 1, 4, 9, 16, 36, 144, 1600, 14930496

Offset: 1

Giovanni Teofilatto, Nov 09 2005

nonn

Any further terms have more than 10,000 digits. - Charles R Greathouse IV, Sep 16 2015

Squares in A084176 (or A059389). Cf. A000045, A179334.

Fibs:= {seq(combinat:-fibonacci(i),i=0..100)}:
sort(convert(select(issqr,{seq(seq(Fibs[i]+Fibs[j],j=1..i),i=1..100)}),list)); # Robert Israel, Jun 03 2024

Select[Union[Total/@Subsets[Fibonacci[Range[0,100]],{2}],Table[Fibonacci[n]*2,{n,0,100}]],IntegerQ[Sqrt[#]]&] (* James C. McMahon, Jun 03 2024 *)

list(lim)=my(F=List(),v=List([0,1]),n=1,t); while((t=fibonacci(n++))<=lim, listput(F,t)); F=Vec(F); for(i=1,#F,for(j=i,#F, if(issquare(t=F[i]+F[j]), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Sep 16 2015

1600 from Jonathan Vos Post, Nov 11 2005

14930496 from N. J. A. Sloane, Nov 11 2005

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

Original entry on oeis.org

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

Carmine Suriano, Jan 12 2011

nonn

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.

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

Cf. A000045, A000290, A179334.

cp's OEIS Frontend

A111378 Squares that are equal to the sum of two Fibonacci numbers.

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