cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 07 2014

Keywords

Comments

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.

Links

Crossrefs

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

Programs

Formula

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

A153239 Balance of binary trees as ordered by A014486: number of vertices in the right subtree minus number of vertices in the left subtree.

Original entry on oeis.org

0, 0, 1, -1, 2, 2, 0, -2, -2, 3, 3, 3, 3, 3, 1, 1, -1, -3, -3, -1, -3, -3, -3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 0, 0, -2, -4, -4, -2, -4, -4, -4, 0, 0, -2, -4, -4, -2, -4, -4, -4, -2, -4, -4, -4, -4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
Offset: 0

Views

Author

Antti Karttunen, Dec 21 2008

Keywords

Comments

Note that for all n, Sum_{i=A014137(n)}^A014138(n) a(i) = 0.

Examples

			A014486(19) encodes the following binary tree:
.\/
..\/.\/
...\./
Because the subtree at the right contains just one internal node and the subtree at the left contains two, we have a(19) = 1-2 = -1.

Links

Crossrefs

A153243 gives the positions of zeros. Cf. A153240, A153241.

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

Views

Author

Antti Karttunen, Dec 21 2008

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

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.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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