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 1-10 of 12 results. Next

A080292 Orbit size of each tree A080293(n) under Donaghey's "Map M" Catalan automorphism.

Original entry on oeis.org

1, 3, 9, 9, 81, 81, 81, 27, 1701, 1701, 1701, 1701, 2673, 2673, 891, 891
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

This is the size of the cycle containing A080295(n) in the permutations A057505/A057506.

Crossrefs

A080977(n) = A080272(2*n)/a(n). A080302(n) = a(n)/3 for n>0. Cf. A080973/A080975.

Formula

a(n) = A080967(A080295(n))

A080318 Breadth-first-wise A014486-like encoding of the branch-reduced binomial-mod-2 binary trees (A080293).

Original entry on oeis.org

2, 56, 16256, 4186496, 274374557696, 70239893062016, 4603241631720636416, 301678043576445270327296, 1295697331082095312130350876983296, 331698516757016399905370236824584576
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

A080297 Orbit size of each tree A080293(n) under Meeussen's bf<->df map on binary trees.

Original entry on oeis.org

1, 3, 202, 41888
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

This is the size of the cycle containing A080295(n) in the permutations A057117/A057118.

Crossrefs

Cf. A080273, A080274.

Formula

a(n) = A080311(A080295(n)).

A080296 a(n) = A080301(A080293(n)).

Original entry on oeis.org

0, 2, 280, 47104, 1552115753, 320620847201, 14010400861700086, 666566814219424468355, 1738670860867061382977091021290, 403468080959285491446589623771973
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Crossrefs

Cf. A080295.

A080263 A014486-encoding of the branch-reduced binomial-mod-2 binary trees.

Original entry on oeis.org

2, 50, 906, 247986, 4072138, 1059204274, 272900475786, 17953590946285746, 287705670922216138, 73724537815637830834, 18880972926031430339466, 1237678872789190922262530226, 316876593058175709191975346890
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

These trees are obtained from the successive generations of Rule 90 cellular automaton (A070886) or Pascal's triangle computed modulo 2 (A047999), with alive cells of the automaton (respectively: the odd binomials) forming the vertices of the zigzag tree.

References

  • J. C. P. Miller, Periodic Forests of Stunted Trees, Phil. Tran. Roy. Soc. London A266 (1970) 63; A293 (1980) 48.

Links

Crossrefs

Same sequence in binary: A080264. Cf. A080265. Breadth-first-wise encodings of the same trees: A080268. Corresponding branch-reduced zigzag trees: A080293.
Number of edges in general trees/internal nodes in binary trees: A006046, number of zigzag-edges (those colored black in illustrations) is one less: A074330. Cf. A080978.

A080973 A014486-encoding of the "Moose trees".

Original entry on oeis.org

2, 52, 14952, 4007632, 268874213792, 68836555442592, 4561331969745081152, 300550070677246403229312, 1294530259719904904564091957759232, 331402554328705507772604330809117952
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

Meeussen's observation about the orbits of a composition of two involutions F and R states that if the orbit size of the composition (acting on a particular element of the set) is odd, then it contains an element fixed by the other involution if and only if it contains also an element fixed by the other, on the (almost) opposite side of the cycle. Here those two involutions are A057163 and A057164, their composition is Donaghey's "Map M" A057505 and as the trees A080293/A080295 are symmetric as binary trees and the cycle sizes A080292 are odd, it follows that these are symmetric as general trees.

Links

Crossrefs

Same sequence in binary: A080974. A036044(a(n)) = a(n) for all n. The number of edges (as general trees): A080978.

Formula

a(n) = A014486(A080975(n)) = A014486(A057505^((A080292(n)+1)/2) (A080293(n))) [where ^ stands for the repeated applications of permutation A057505.]

A080295 A014486-index of the branch-reduced binomial-mod-2 binary trees.

Original entry on oeis.org

1, 6, 477, 70818, 2208159610, 445557105328, 19185898282602827, 905428099582719818595
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Crossrefs

Cf. A014486, A080265, A080293, A080296, A080300, A080320, A080979.

Formula

a(n) = A080298(A080265(n)).
a(n) = A080979(A080265(2*n)).
a(n) = A080300(A080293(n)).

A080979 Each tree encoded in A014486 mapped to the corresponding branch-reduced zigzag-tree (positions in A014486).

Original entry on oeis.org

0, 1, 2, 3, 2, 5, 6, 7, 3, 2, 5, 11, 12, 5, 6, 15, 16, 7, 18, 6, 20, 7, 3, 2, 5, 11, 12, 5, 11, 29, 30, 12, 32, 11, 34, 12, 5, 6, 15, 39, 40, 15, 16, 43, 16, 7, 18, 47, 48, 49, 18, 6, 15, 53, 20, 55, 16, 57, 7, 18, 6, 20, 20, 7, 3, 2, 5, 11, 12, 5, 11, 29, 30, 12, 32, 11, 34, 12, 5, 11, 29
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

For trees which are already branch-reduced we have a(n)=n, where n is one of A080980.

Links

Crossrefs

Same sequence sorted, with duplicates removed: A080980. Cf. A080293.

A080975 A014486-index of the "Moose trees".

Original entry on oeis.org

1, 7, 515, 73211, 2249220471, 431283926958, 18838905762720934, 896134321804401371660, 2333852111980919691995847581921, 537961368577436933017494169487235
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

See A080973 for illustration and comments.

Crossrefs

A057164(a(n)) = a(n) for all n. Cf. A080976.

Formula

a(n) = A057505^((A080292(n)+1)/2) (A080293(n)) [where ^ stands for the repeated applications of permutation A057505.]

A080294 A063171-encoding of the branch-reduced binomial-mod-2 binary trees.

Original entry on oeis.org

10, 110010, 11100100110010, 1111001001001100110010, 11111001001100100100110011100100110010, 1111110010010011001001001100111001001100110010
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Crossrefs

Same sequence in decimal: A080293. Breadth-first-wise encoding: A080319.

Formula

a(n) = A007088(A080293(n)).
Showing 1-10 of 12 results. Next

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