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

Author

Antti Karttunen, Oct 10 2016

Keywords

• nonn

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

Crossrefs

Cf. A001221, A002487, A069010, A073491, A125184, A243055, A260443, A277020.

Programs

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)))))))

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).