A080300 -id:A080300 - cp's OEIS frontend

A080270 Positions of A080268 in A014486.

Original entry on oeis.org

1, 8, 62, 6213, 72665, 11517948

Offset: 0

Antti Karttunen, Mar 02 2003

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

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

A082859 Lower triangular region of A082858.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 1, 1, 3, 0, 1, 2, 1, 4, 0, 1, 2, 1, 2, 5, 0, 1, 2, 3, 2, 2, 6, 0, 1, 1, 3, 1, 1, 3, 7, 0, 1, 1, 3, 1, 1, 3, 3, 8, 0, 1, 2, 1, 4, 2, 2, 1, 1, 9, 0, 1, 2, 1, 4, 2, 2, 1, 1, 4, 10, 0, 1, 2, 1, 4, 5, 2, 1, 1, 4, 4, 11, 0, 1, 2, 1, 2, 5, 2, 1, 1, 2, 2, 5, 12, 0, 1, 2, 1, 2, 5, 2, 1, 1, 2, 2, 5, 5, 13, 0, 1, 2, 3, 4, 2, 6, 3, 3, 4, 4, 4, 2, 2, 14

Offset: 0

Antti Karttunen, May 06 2003

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)

Cf. A082861, A003056, A002262.

A082861 Lower triangular region of A082860.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 3, 3, 6, 3, 4, 4, 4, 14, 4, 5, 5, 5, 15, 11, 5, 6, 6, 6, 6, 14, 15, 6, 7, 7, 16, 7, 42, 43, 16, 7, 8, 8, 19, 8, 51, 52, 19, 20, 8, 9, 9, 9, 37, 9, 28, 37, 121, 149, 9, 10, 10, 10, 38, 10, 29, 38, 122, 150, 25, 10, 11, 11, 11, 39, 11, 11, 39, 123, 151, 28, 29, 11, 12, 12, 12, 40, 30, 12, 40, 124, 152, 84, 85, 30, 12, 13, 13, 13, 41, 33, 13, 41, 125, 153

Offset: 0

Antti Karttunen, May 06 2003

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)

Cf. A082859, A003056, A002262.

A083938 A014486-indices of binary trees whose left and right subtree are identical.

Original entry on oeis.org

0, 1, 6, 42, 52, 385, 414, 477, 506, 555, 4089, 4180, 4388, 4479, 4645, 5095, 5186, 5394, 5485, 5651, 5969, 6060, 6226, 6502, 47363, 47661, 48366, 48664, 49237, 50800, 51098, 51803, 52101, 52674, 53808, 54106, 54679, 55681, 59311, 59609, 60314

Offset: 0

Antti Karttunen, May 13 2003

nonn

Fixed points of permutation A069770. Diagonal of A072764 (and A072766).

a(n) = A080300(A083939(n)). Cf. A083940.

a(0)=0, a(n)=A072764bi(n-1, n-1).

A083940 A014486-indices of symmetric binary trees.

Original entry on oeis.org

0, 1, 6, 43, 51, 389, 416, 477, 504, 551, 4102, 4191, 4397, 4485, 4649, 5100, 5187, 5393, 5481, 5645, 5964, 6051, 6215, 6489, 47404, 47700, 48403, 48697, 49268, 50833, 51126, 51828, 52120, 52691, 53829, 54120, 54690, 55690, 59334, 59627, 60328

Offset: 0

Antti Karttunen, May 13 2003

nonn

Fixed points of permutation A057163.

a(n) = A080300(A083941(n)). Cf. A083938, A084108.

a(0)=0, a(n)=A072764bi(n-1, A057163(n-1)).

A085200 Inverse function of N -> N injection A071155.

Original entry on oeis.org

0, 1, 0, 2, 0, 3, 0, 0, 0, 4, 0, 6, 0, 0, 0, 5, 0, 7, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 14, 0, 0, 0, 11, 0, 16, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 15, 0, 0, 0, 12, 0, 17, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 18, 0, 0, 0, 0, 0, 21, 0, 0, 0

Offset: 0

Antti Karttunen, Jun 23 2003

nonn

a(0)=0 because A071155(0)=0, but a(n) = 0 also for those n which do not occur as values of A071155. All positive natural numbers occur here once.

a(A071155(n)) = n for all n. Cf. A080300.

A126310 A014486-index for the Dyck path "derived" from the n-th Dyck path encoded by A014486(n).

Original entry on oeis.org

0, 0, 1, 0, 2, 1, 1, 1, 0, 4, 2, 2, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 0, 9, 4, 4, 4, 2, 4, 2, 4, 5, 2, 2, 2, 2, 1, 4, 2, 2, 2, 1, 4, 2, 6, 7, 3, 2, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 1, 1, 1, 1, 0, 23, 9, 9, 9, 4, 9, 4, 9, 10, 4, 4, 4, 4, 2, 9, 4, 4, 4, 2, 9, 4, 11, 12, 5, 4, 4, 5, 2, 4, 2, 4, 5, 2, 4, 5, 5

Offset: 0

Antti Karttunen, Jan 02 2007

nonn

According to Vaillé, the concept of "dérivation des ponts" is defined by Kreweras, in "Sur les éventails de segments" paper.

G. Kreweras, Sur les éventails de segments, Cahiers du Bureau Universitaire de Recherche Opérationelle, Cahier no. 15, Paris, 1970, pp. 3-41.
J. Vaillé, Une Bijection Explicative de Plusieurs Propriétés Remarquables des Ponts, European J. Combin. 18 (1997), no. 1, 117-124.

Cf. A125986, A126309, A125985.

a(n) = A125986(A126309(A125985(n))).

A209643 A014486-indices for rooted plane trees where non-leaf branching can occur only at the leftmost branch of any level, but nowhere else.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 17, 19, 20, 21, 22, 23, 37, 42, 44, 45, 51, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 65, 107, 121, 126, 128, 129, 149, 154, 156, 157, 163, 165, 166, 168, 169, 170, 177, 179, 180, 182, 183, 184, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 329, 371, 385, 390, 392, 393, 461, 475, 480, 482

Offset: 0

Antti Karttunen, Mar 24 2012

nonn

5 is not member of this sequence, as it encodes in A014486 a general tree:
..|
\/
which has a nonempty branch which is not the leftmost child of its parent vertex.

Antti Karttunen, Table of n, a(n) for n = 0..32767
A. Karttunen, Corresponding trees illustrated on 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 17th, etc. row in this illustration.

Cf. A209644, A071163.

a(n) = A080300(A209641(n)).

A083934 A014486-indices of A083932-trees.

Original entry on oeis.org

0, 3, 15, 22, 113, 120, 178, 185, 196, 1103, 1110, 1168, 1175, 1186, 1787, 1794, 1852, 1859, 1870, 2022, 2029, 2040, 2055, 12257, 12264, 12322, 12329, 12340, 12941, 12948, 13006, 13013, 13024, 13176, 13183, 13194, 13209, 20122, 20129, 20187

Offset: 0

Antti Karttunen, May 13 2003

nonn

Cf. A014486, A080300, A083932.

Inverse function: A083935.

a(n) = A080300(A083932(n)).

A083942 Positions of breadth-first-wise encodings (A002542) of the complete binary trees (A084107) in A014486.

Original entry on oeis.org

0, 1, 8, 625, 13402696, 19720133460129649, 126747521841153485025455279433135688, 15141471069096667541622192498608408980462133134430650704600552060872705905

Offset: 0

Antti Karttunen, May 13 2003

nonn

Alexander Adamchuk, Nov 10 2007, Table of n, a(n) for n = 0..11
Eric Weisstein's World of Mathematics, Catalan Number.

Cf. A014138 (partial sums of Catalan numbers), A000108 (Catalan Numbers).

a(n) = A057118(A084108(n)).
a(n) = A080300(A002542(n)) [provided that 2^((2^n)-1)*((2^((2^n)-1))-1) is indeed the formula for A002542].
Conjecture: a(n) = A014138(2^n-2) for n>0. - Alexander Adamchuk, Nov 10 2007
Conjecture: a(n) = Sum_{k=1..2^n-1} A000108(k). - Alexander Adamchuk, Nov 10 2007
Let h(n) = -((C(2*n,n)*hypergeom([1,1/2+n],[2+n],4))/(1+n)+I*sqrt(3)/2+1/2). Assuming Adamchuk's conjecture a(n) = h(2^n) and A014138(n) = h(n+1). - Peter Luschny, Mar 09 2015

cp's OEIS Frontend

A080270 Positions of A080268 in A014486.

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A082859 Lower triangular region of A082858.

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A082861 Lower triangular region of A082860.

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A083938 A014486-indices of binary trees whose left and right subtree are identical.

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A083940 A014486-indices of symmetric binary trees.

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A085200 Inverse function of N -> N injection A071155.

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A126310 A014486-index for the Dyck path "derived" from the n-th Dyck path encoded by A014486(n).

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A209643 A014486-indices for rooted plane trees where non-leaf branching can occur only at the leftmost branch of any level, but nowhere else.

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A083934 A014486-indices of A083932-trees.

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A083942 Positions of breadth-first-wise encodings (A002542) of the complete binary trees (A084107) in A014486.

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