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A153241
Balance of general trees as ordered by A014486, variant B.
4
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
OFFSET
0,13
COMMENTS
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.
Note that for all n, Sum_{i=A014137(n)}^A014138(n) a(i) = 0.
LINKS
PROG
(Scheme)
(define (A153241 n) (gentree-balance (A014486->parenthesization (A014486 n))))
(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))))))
CROSSREFS
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.
Sequence in context: A083570 A287407 A153240 * A306863 A334108 A332813
KEYWORD
sign
AUTHOR
Antti Karttunen, Dec 21 2008
STATUS
approved