A045702 Sums of two squares of Fibonacci numbers.

0, 1, 2, 4, 5, 8, 9, 10, 13, 18, 25, 26, 29, 34, 50, 64, 65, 68, 73, 89, 128, 169, 170, 173, 178, 194, 233, 338, 441, 442, 445, 450, 466, 505, 610, 882, 1156, 1157, 1160, 1165, 1181, 1220, 1325, 1597, 2312, 3025, 3026, 3029, 3034, 3050, 3089, 3194, 3466

Offset: 1

Author

Felice Russo

Keywords

• nonn
• easy
• nice

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to sums of squares

Programs

Mathematica

Take[Union[Total/@Tuples[Fibonacci[Range[0,15]]^2,{2}]],60]  (* Harvey P. Dale, Jan 17 2011 *)

PARI

list(lim)=my(sq=sqrtint(lim\=1),v=List(),f=List([0,1]),t); while((t=f[#f]+f[#f-1])<=sq, listput(f,t)); f=apply(sqr,f); for(i=1,#f, for(j=1,i, t=f[i]+f[j]; if(t>lim, break); listput(v,t))); Set(v) \\ Charles R Greathouse IV, Jun 27 2017

Formula

a(4)=5 because 5 = 1^2 + 2^2;

a(8)=13 because 13 = 2^2 + 3^2.