A117942 a(n) = a(3n) = -a(3n+1) = -a(3n+2)/2.

1, -1, -2, -1, 1, 2, -2, 2, 4, -1, 1, 2, 1, -1, -2, 2, -2, -4, -2, 2, 4, 2, -2, -4, 4, -4, -8, -1, 1, 2, 1, -1, -2, 2, -2, -4, 1, -1, -2, -1, 1, 2, -2, 2, 4, 2, -2, -4, -2, 2, 4, -4, 4, 8, -2, 2, 4, 2, -2, -4, 4, -4, -8, 2, -2, -4, -2, 2, 4, -4, 4, 8, 4, -4, -8, -4, 4, 8, -8, 8, 16, -1, 1, 2, 1, -1, -2, 2, -2, -4, 1, -1

Offset: 0

Author

Paul Barry, Apr 05 2006

Keywords

• sign

Comments

a(n) = a(3n)/a(0) = a(3n+1)/a(1) = a(3n+2)/a(2).

Row sums of A117941.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19683

Crossrefs

Cf. A117592 (gives the absolute values).

Cf. A062756, A081603.

Programs

Scheme

;; A stand-alone recurrence:
(define (A117942 n) (cond ((zero? n) 1) ((zero? (modulo n 3)) (A117942 (/ n 3))) (else (let ((d (modulo n 3))) (- (* d (A117942 (/ (- n d) 3))))))))
;; An implementation based on a new formula:

Scheme

(define (A117942 n) (* (A000079 (A081603 n)) (expt -1 (+ (A062756 n) (A081603 n)))))
;; Antti Karttunen, Jul 26 2017

Formula

a(n) = 2^A081603(n) * (-1)^(A062756(n)+A081603(n)). - Antti Karttunen, Jul 26 2017

Extensions

More terms from Antti Karttunen, Jul 26 2017