A277325 Product of nonzero coefficients of the n-th Stern polynomial.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 4, 1, 1, 1, 2, 2, 9, 2, 12, 3, 6, 1, 6, 4, 9, 1, 8, 1, 1, 1, 2, 2, 18, 2, 20, 9, 24, 2, 32, 12, 30, 3, 40, 6, 12, 1, 12, 6, 45, 4, 60, 9, 24, 1, 18, 8, 27, 1, 16, 1, 1, 1, 2, 2, 36, 2, 60, 18, 48, 2, 72, 20, 160, 9, 140, 24, 72, 2, 96, 32, 200, 12, 240, 30, 140, 3, 120, 40, 160, 6, 160, 12, 24, 1

Offset

0,6

Comments

a(n) = product of nonzero terms on the n-th row of A125184.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Formula

a(n) = A005361(A260443(n)).

a(n) = A227349(A277020(n)).

a(2n) = a(n).

a(n) >= A277326(n).

Prog

(Scheme)
(define (A277325 n) (A005361 (A260443 n)))
;; A standalone implementation:
(define (A277325 n) (reduce * 1 (filter positive? (A260443as_coeff_list n))))
(definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))
(define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

Crossrefs

Cf. A005361, A125184, A227349, A260443, A277020.

Cf. also A277326 (lcm of nonzero coefficients) and A002487 (their sum).

Sequence in context: A050431 A051574 A029386 * A240837 A369376 A060502

Adjacent sequences: A277322 A277323 A277324 * A277326 A277327 A277328

Keyword

nonn

Author

Antti Karttunen, Oct 13 2016

Status

approved