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

%I A277314 #16 Oct 13 2016 10:30:20
%S A277314 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,
%T A277314 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,
%U A277314 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
%N A277314 Number of nonzero coefficients in Stern polynomial B(n,t).
%C A277314 a(n) is the number of nonzero terms on row n of A125184.
%H A277314 Antti Karttunen, <a href="/A277314/b277314.txt">Table of n, a(n) for n = 0..8192</a>
%F A277314 a(n) = A001221(A260443(n)).
%F A277314 a(n) = A069010(A277020(n)).
%F A277314 a(n) = 1 + A243055(A260443(n)). [Because each term of A260443 is in A073491.]
%F A277314 a(2n) = a(n).
%F A277314 For all n >= 0 , a(n) <= A002487(n).
%o A277314 (Scheme)
%o A277314 (define (A277314 n) (A001221 (A260443 n)))
%o A277314 ;; Or as a standalone program:
%o A277314 (define (A277314 n) (length (filter positive? (A260443as_coeff_list n))))
%o A277314 (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))))))
%o A277314 (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)))))))
%Y A277314 Cf. A001221, A002487, A069010, A073491, A125184, A243055, A260443, A277020.
%K A277314 nonn
%O A277314 0,4
%A A277314 _Antti Karttunen_, Oct 10 2016