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A153241
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Balance of general trees as ordered by A014486, variant B.
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4
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0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, 0, 2, 2, -1, 0, -2, 0, 1, -2, -1, 0, 0, 0, 1, 1, 2, 2, -1, 1, 0, 3, 3, 0, 3, 3, 3, -1, 0, -1, 1, 1, -2, -1, -3, 0, 1, -3, 0, 2, 2, -2, -1, -3, -1, 0, -3, -2, 0, 1, -3, -2, -1, 0, 0, 0, 1, 1, 2, 2, 0, 2, 2, 3, 3, 2, 3, 3, 3, -1, 0, 0, 2, 2, -2, 1, 0, 4, 4, 1, 4
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OFFSET
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0,13
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COMMENTS
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This differs from variant A153240 only in that if the degree of the tree is odd (i.e. A057515(n) = 1 mod 2), then the balance of the center-subtree is taken into account ONLY if the total weight of other subtrees at the left and the right hand side from the center were balanced against each other.
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LINKS
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PROG
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(MIT Scheme:)
(define (gentree-balance l) (let ((r (reverse l))) (let loop ((i 0) (j (- (length l) 1)) (l l) (r r) (z 0)) (cond ((= i j) (+ z (if (zero? z) (gentree-balance (car l)) 0))) ((> i j) z) (else (loop (+ i 1) (- j 1) (cdr l) (cdr r) (+ z (- (count-pars (car r)) (count-pars (car l))))))))))
(define (count-pars a) (cond ((not (pair? a)) 0) (else (+ 1 (count-pars (car a)) (count-pars (cdr a))))))
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CROSSREFS
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Differs from variant A153240 for the first time at n=268, where A153240(268) = 2, while a(268)=1. Note that (A014486->parenthesization (A014486 268)) = (() (() (())) (())). a(A061856(n)) = 0 for all n. Cf. also A153239.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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