A117942 - OEIS

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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

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OFFSET

0,3

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

FORMULA

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

PROG

(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

CROSSREFS

Cf. A117592 (gives the absolute values).

Cf. A062756, A081603.

Sequence in context: A145788 A323861 A117592 * A290092 A066877 A240071

Adjacent sequences: A117939 A117940 A117941 * A117943 A117944 A117945

KEYWORD

sign

AUTHOR

Paul Barry, Apr 05 2006

EXTENSIONS

More terms from Antti Karttunen, Jul 26 2017

STATUS

approved