A153239 -id:A153239 - cp's OEIS frontend

A243492 Difference A243491(n) - A127301(n).

0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 2, -2, 0, 7, 4, 0, -7, -4, 7, 0, -7, 0, 0, 0, 4, -4, 0, 14, 8, 0, -14, -8, 14, 0, -14, 0, 29, 19, 25, 16, 14, 10, 5, -10, -29, -19, -5, -16, -25, -14, 47, 26, 17, 0, 0, 0, -17, -47, -26, 37, 12, -12, -37, 0, 0, 0, 8, -8, 0, 28, 16, 0, -28, -16, 28, 0, -28, 0

Offset: 0

Antti Karttunen, Jun 07 2014

A243490 gives the positions of zeros, which are also the fixed points of A069787. They correspond to the dots shown on the y=0 line of the arcsinh-version of scatter plot.

Antti Karttunen, Table of n, a(n) for n = 0..6917
A. Karttunen, On the fixed points of A071661 (Notes in OEIS Wiki)

Cf. A069787, A243490, A057505, A079438, A123050, A080070, A153239, A153240, A153241, A154477.

(define (A243492 n) (- (A243491 n) (A127301 n)))

a(n) = A243491(n) - A127301(n) = A127301(A069787(n)) - A127301(n).

A153240 Balance of general trees as ordered by A014486, variant A.

Original entry on oeis.org

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

Antti Karttunen, Dec 21 2008

sign

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.

			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.

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

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.

A153241 Balance of general trees as ordered by A014486, variant B.

Original entry on oeis.org

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

Antti Karttunen, Dec 21 2008

sign

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

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.

A153243 Positions of balanced binary trees in A014486, i.e., trees where number of vertices in the right subtree = number of vertices in the left subtree.

Original entry on oeis.org

0, 1, 6, 42, 43, 51, 52, 385, 386, 387, 388, 389, 413, 414, 415, 416, 417, 475, 476, 477, 478, 479, 503, 504, 505, 506, 507, 551, 552, 553, 554, 555, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 4100, 4101, 4102, 4179, 4180

Offset: 0

Antti Karttunen, Dec 21 2008

nonn

Positions of zeros in A153239.

cp's OEIS Frontend

A243492 Difference A243491(n) - A127301(n).

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A153240 Balance of general trees as ordered by A014486, variant A.

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A153241 Balance of general trees as ordered by A014486, variant B.

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A153243 Positions of balanced binary trees in A014486, i.e., trees where number of vertices in the right subtree = number of vertices in the left subtree.

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