A277314 Number of nonzero coefficients in Stern polynomial B(n,t).

0, 1, 1, 2, 1, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 4, 1, 4, 3, 3, 2, 3, 3, 4, 2, 4, 3, 4, 3, 4, 4, 5, 1, 5, 4, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 4, 5, 2, 5, 4, 4, 3, 4, 4, 5, 3, 5, 4, 5, 4, 5, 5, 6, 1, 6, 5, 5, 4, 5, 4, 5, 3, 5, 4, 4, 3, 4, 4, 5, 2, 5, 4, 4, 3, 4, 4, 5, 3, 5, 4, 5, 4, 5, 5, 6, 2, 6, 5, 5, 4, 5, 4, 5, 3, 5, 4, 5, 4, 5, 5, 6, 3, 6, 5, 5, 4, 5, 5, 6, 4

Offset

0,4

Comments

a(n) is the number of nonzero terms on row n of A125184.

Links

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

Formula

a(n) = A001221(A260443(n)).

a(n) = A069010(A277020(n)).

a(n) = 1 + A243055(A260443(n)). [Because each term of A260443 is in A073491.]

a(2n) = a(n).

For all n >= 0 , a(n) <= A002487(n).

Prog

(Scheme)
(define (A277314 n) (A001221 (A260443 n)))
;; Or as a standalone program:
(define (A277314 n) (length (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. A001221, A002487, A069010, A073491, A125184, A243055, A260443, A277020.

Sequence in context: A355733 A256757 A333860 * A120562 A178692 A364144

Adjacent sequences: A277311 A277312 A277313 * A277315 A277316 A277317

Keyword

nonn

Author

Antti Karttunen, Oct 10 2016

Status

approved