A080979 -id:A080979 - cp's OEIS frontend

A080972 a(n) = A080969(n)/A080967(A080979(A080970(n))).

1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 1, 4, 1, 2, 1, 2, 2, 3, 3, 1, 2, 2, 1, 2, 4, 1, 1, 2, 1, 4, 4, 1, 2, 2, 1, 2, 4, 1, 2, 4, 2, 4, 1, 1, 4, 4, 1, 4, 1, 2, 1, 4, 4, 2, 1, 4, 4, 2, 4, 4, 2, 1

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

Donaghey shows in his paper that the orbit size (under the automorphism A057505/A057506) of each non-branch-reduced tree encoded by A080971(n) is divisible by the orbit size of the corresponding branch-reduced tree. This sequence gives the corresponding ratio.

Robert Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.

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

Antti Karttunen, Mar 02 2003

nonn

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.

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

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

Antti Karttunen, Mar 02 2003

nonn

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

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

A080980 A014486-indices of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey).

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 11, 12, 15, 16, 18, 20, 29, 30, 32, 34, 39, 40, 43, 47, 48, 49, 53, 55, 57, 81, 82, 85, 89, 90, 91, 95, 97, 99, 113, 114, 116, 118, 123, 124, 136, 137, 139, 140, 141, 143, 146, 155, 159, 160, 161, 165, 167, 173, 183, 245, 246, 248, 250, 255, 256, 268

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

Robert Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.
R. P. Stanley, Exercises on Catalan and Related Numbers

Cf. A080979. a(n) = A080300(A080981(n)). See comment at A080981. Complement of A080970.

cp's OEIS Frontend

A080972 a(n) = A080969(n)/A080967(A080979(A080970(n))).

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

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

Views

Author

Keywords

Crossrefs

Formula

A080980 A014486-indices of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey).

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Author

Keywords

Links

Crossrefs