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 1-6 of 6 results.

A080320 a(n) = A057118(A080295(n)) = A080300(A080318(n)). Positions of A080318 in A014486.

Original entry on oeis.org

1, 8, 625, 82461, 2414517826, 465696894874, 19586243923520645, 911881322544255111111, 2344958374133795816706574529598, 540549352213084909964319555106232
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Crossrefs

Cf. A080321.

A080293 A014486-encoding of the branch-reduced binomial-mod-2 binary trees.

Original entry on oeis.org

2, 50, 14642, 3969842, 267572689202, 69427226972978, 4581045692538239282, 301220569271221714981682, 1295918094920364850246919050705202, 332029112115571675270693117549056818
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

These are obtained from the stunted binomial-mod-2 zigzag trees (A080263) either by extending each leaf to a branch of two leaves, or by branch-reducing every other such tree.

Crossrefs

a(n) = A014486(A080295(n)). Same sequence in binary: A080294. Breadth-first-wise encoding: A080318. "Moose-trees" obtained from these: A080973. Cf. A080292, A080297.

Formula

a(n) = A080310(A080263(n)) = A014486(A080298(A080265(n))) = A014486(A080979(A080265(2*n)))

A080973 A014486-encoding of the "Moose trees".

Original entry on oeis.org

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

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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.]

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

Views

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))

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.
Showing 1-6 of 6 results.

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

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