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Search: id:A153240
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| A153240 |
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Balance of general trees as ordered by A014486, variant A. |
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+0
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
(list; graph; listen)
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OFFSET
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0,13
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COMMENT
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This differs from variant A153241 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 always taken into account.
Note that for all n, Sum_{i=A014137(n)}^A014138(n) a(i) = 0.
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..2055
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EXAMPLE
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A014486(25) encodes the following general tree:
......o
......|
o.o...o.o
.\.\././
....*..
which consists of four subtrees, of which the second from right is one larger than the others, so we have a(25) = (0+1)-(0+0) = 1.
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PROGRAM
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(MIT Scheme:)
(define (A153240 n) (gentree-deep-balance (A014486->parenthesization (A014486 n))))
(define (gentree-deep-balance l) (let ((r (reverse l))) (let loop ((i 0) (j (- (length l) 1)) (l l) (r r) (z 0)) (cond ((= i j) (+ z (gentree-deep-balance (car l)))) ((> 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 A153241 for the first time at n=268, where A153241(268) = 1, while a(268)=2. Note that (A014486->parenthesization (A014486 268)) = (() (() (())) (())). a(A061856(n)) = 0 for all n. Cf. also A153239.
Sequence in context: A133624 A030110 A083570 this_sequence A153241 A096830 A141647
Adjacent sequences: A153237 A153238 A153239 this_sequence A153241 A153242 A153243
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KEYWORD
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sign
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 21 2008
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