Squares of the Fibonacci numbers

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The squares of the Fibonacci numbers are, you guessed it, the Fibonacci numbers squared. Given a Fibonacci number $F_n$, observe that

$F_{n-1}{F}_{n+1}={F_n}^2+(-1{)}^n.$

For example, $F_4{F}_6=3\times 8=5^2+(-1{)}^5=(F_5{)}^2-1=24,$ and $F_5{F}_7=5\times 13=8^2+(-1{)}^6=(F_6{)}^2+1=65.$

Sequences

A007598 Squared Fibonacci numbers: $F(n{)}^2$ where $F(n)=$ A000045$(n),n\ge 0.$

{0, 1, 1, 4, 9, 25, 64, 169, 441, 1156, 3025, 7921, 20736, 54289, 142129, 372100, 974169, 2550409, 6677056, 17480761, 45765225, 119814916, 313679521, 821223649, 2149991424, ...}

See also

• Fibonacci multiplication table
• Lucas numbers
• Squares of the Lucas numbers