0,13

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.

A. Karttunen, Table of n, a(n) for n = 0..2055

(MIT 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))))))

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: A030110 A083570 A153240 this_sequence A096830 A141647 A001617

Adjacent sequences: A153238 A153239 A153240 this_sequence A153242 A153243 A153244

sign

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 21 2008