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 1-7 of 7 results.

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

Views

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.

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

Views

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)))

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)).

A080270 Positions of A080268 in A014486.

Original entry on oeis.org

1, 8, 62, 6213, 72665, 11517948
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Crossrefs

a(n) = A080300(A080268(n)). Cf. A080271.

Formula

a(n) = A057118(A080265(n)).

A080272 Orbit size of each tree A080263(n) under Donaghey's "Map M" Catalan automorphism.

Original entry on oeis.org

1, 3, 3, 27, 54, 54, 18, 1134, 1134, 1134, 1134, 1782, 1782, 594, 594, 30618, 30618, 30618, 30618, 78246, 78246, 78246, 78246, 165726, 165726
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

This is the size of the cycle containing A080265(n) in the permutations A057505/A057506.

Crossrefs

A080977(n) = a(2*n)/A080292(n).

Formula

a(n) = A080967(A080265(n)).

A080273 Orbit size of each tree A080263(n) under Meeussen's bf<->df map on binary trees.

Original entry on oeis.org

1, 3, 16, 1441, 41888, 3376173
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

This is the size of the cycle containing A080265(n) in the permutations A057117/A057118.

Crossrefs

Cf. A080274, A080297.

Formula

a(n) = A080311(A080265(n)).

A080266 a(n) = A080301(A080263(n)).

Original entry on oeis.org

0, 2, 28, 3995, 53032, 9218158, 1716408828, 68406706423034, 993609159645474, 211483814340246174, 45849905806140642231, 2254554272777258549734599, 509234594705250632023415288, 26692711238971831653512953923634
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Crossrefs

Cf. A080265.
Showing 1-7 of 7 results.

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