```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ``` ```; lucas sequences (define (lucas l2 l1 n) (let loop ((n n) (l2 l2) (l1 l1) (ls (list l1 l2))) (if (zero? n) (reverse ls) (let ((l (+ l1 l2))) (loop (- n 1) l1 l (cons l ls)))))) (display (lucas 1 1 20)) (newline) ; fibonacci numbers (display (lucas 1 3 20)) (newline) ; lucas numbers (define (lucas p q l2 l1 n) (let loop ((n n) (l2 l2) (l1 l1) (ls (list l1 l2))) (if (zero? n) (reverse ls) (let ((l (- (* p l1) (* q l2)))) (loop (- n 1) l1 l (cons l ls)))))) (display (lucas 1 -1 1 1 20)) (newline) ; fibonacci numbers (display (lucas 1 -1 1 3 20)) (newline) ; lucas numbers (define (u n p q) (if (< n 1) 1 (if (= n 1) p (let ((k (quotient n 2))) (if (odd? n) (- (* (u (+ k 1) p q) (v k p q)) (expt q k)) (* (u k p q) (v k p q))))))) (define (v n p q) (if (< n 1) 2 (if (= n 1) p (let ((k (quotient n 2))) (if (odd? n) (- (* (v (+ k 1) p q) (v k p q)) (* p (expt q k))) (- (expt (v k p q) 2) (* 2 (expt q k)))))))) (display (u 22 1 -1)) (newline) ; fibonacci (display (v 22 1 -1)) (newline) ; lucas ```
 ```1 2 3 4 5 6 ``` ```(1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711) (1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603) (1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711) (1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603) 17711 39603 ```