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## Main Question or Discussion Point

Can someone guide me on how to prove that

[tex]F_{4n+3} + F_{4n+6} = F_{2n+1}^2 + F_{2n+4}^2[/tex]

either side of the above is the difference

[tex](F_{2n+2}*F_{2n+3} + F_{2n+4}^2) - (F_{2n}*F_{2n+1} + F_{2n+2}^2)[/tex]

I intend to post this sequence [tex]F_{2n}*F_{2n+1} + F_{2n+2}^2[/tex], with a comment re a few properties thereof, on Sloane's online encyclopedia of integer sequences but would like to verify the above identity first.

[tex]F_{4n+3} + F_{4n+6} = F_{2n+1}^2 + F_{2n+4}^2[/tex]

either side of the above is the difference

[tex](F_{2n+2}*F_{2n+3} + F_{2n+4}^2) - (F_{2n}*F_{2n+1} + F_{2n+2}^2)[/tex]

I intend to post this sequence [tex]F_{2n}*F_{2n+1} + F_{2n+2}^2[/tex], with a comment re a few properties thereof, on Sloane's online encyclopedia of integer sequences but would like to verify the above identity first.