A218783 -id:A218783 - cp's OEIS frontend

A218777 A014486-indices for the Beanstalk-tree growing one natural number at time, starting from the tree of one internal node (1), with the "lesser numbers to the left hand side" construction.

1, 3, 6, 15, 39, 117, 359, 1149, 3780, 12752, 43740, 152346, 536655, 1909411, 6852153, 24772328, 90137210, 329838392, 1213048022, 4481262944, 16621500330, 61875433940, 231099456721, 865736972546, 3252139562356, 12247622197965, 46232602224402, 174897265479074

Offset: 1

Antti Karttunen, Nov 17 2012

nonn

See comments and examples at A218776.

Antti Karttunen, Table of n, a(n) for n = 1..128

a(n) = A057163(A218779(n)). Cf. A218787, A218776, A218781, A218783.

a(n) = A080300(A218776(n)).

A218779 A014486-indices for the Beanstalk-tree growing one natural number at time, starting from the tree of one internal node (1), with the "lesser numbers to the right hand side" construction.

Original entry on oeis.org

1, 2, 6, 16, 53, 156, 491, 1584, 5286, 17855, 61405, 214012, 754731, 2688307, 9659023, 34947356, 127260566, 465920651, 1714294995, 6335423798, 23506865260, 87534068725, 327024845325, 1225395355165, 4604242172697, 17343284212635, 65480496260109, 247755060623522

Offset: 1

Antti Karttunen, Nov 17 2012

nonn

See comments and examples at A218778.

Antti Karttunen, Table of n, a(n) for n = 1..128

Cf. A218778, A218781, A218783.

a(n) = A080300(A218778(n)).

a(n) = A057163(A218777(n)).

A218782 A014486-codes for the compact representation of Beanstalk-tree, growing by two natural numbers at time, starting from the tree of one internal node (1) and two leaves (3 and 2), with the larger numbers coming to the left hand side.

Original entry on oeis.org

2, 12, 52, 216, 872, 3496, 14024, 56200, 224904, 899720, 3599496, 14398600, 57599112, 230398088, 921606280, 3686471816, 14745933960, 58983782536, 235935438984, 943742064776, 3774970665096, 15099883493512, 60399541098632, 241598171519112, 966392760309896

Offset: 1

Antti Karttunen, Nov 17 2012

nonn

The active middle region of the triangle (see attached "Wolframesque" illustration) corresponds to the area where the growing tip(s) of the beanstalk are located. Successively larger "turbulences" occurring in that area appear approximately at the row numbers given by A218548 divided by two. The larger tendrils, (the finite side-trees) are, the longer there is vacillation in the direction of the growing region, which lasts until the growing tip of the infinite stem (A179016) has passed the topmost tips of the tendril. See also A218612.

These are the mirror-images (in binary tree sense) of the terms in sequence A218780. For less compact versions, see A218778 & A218776.

			Illustration how the growing beanstalk-tree produces the first four terms of this sequence. In this "compact" variant, each successive pair of numbers ((2,3), (4,5), (6,7), etc.) adds a new bud (\/) to the beanstalk, with the lesser numbers coming to the right hand side:
----------
..3...2...
...\./.... Coded by A014486(A218783(1)) = A014486(1) = 2 (binary 10).
....1.....
----------
5...4.....
.\./......
..3...2...
...\./.... Coded by A014486(A218783(2)) = A014486(3) = 12 (bin. 1100).
....1.....
----------
..7...6...
...\./....
5...4.....
.\./......
..3...2...
...\./.... Coded by A014486(A218783(3)) = A014486(7) = 52 (110100).
....1.....
----------
9...8.....
.\./......
..7...6...
...\./....
5...4.....
.\./......
..3...2...
...\./.... Coded by A014486(A218783(4)) = A014486(18) = 216 (11011000).
....1.....
----------
Thus the first four terms of this sequence are 2, 12, 52 and 216.

A. Karttunen, Table of n, a(n) for n = 1..256
A. Karttunen, Terms a(1)-a(4096) drawn as binary strings, in Wolframesque fashion.

a(n) = A014486(A218783(n)). Cf. A014486, A218790, A218778, A218776, A218780, A218788.

A218790 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218782.

Original entry on oeis.org

1, 3, 5, 13, 21, 37, 53, 117, 181, 309, 437, 693, 949, 1717, 1461, 3509, 5557, 9653, 13749, 21941, 30133, 54709, 46517, 79285, 112053, 210357, 177589, 472501, 308661, 734645, 996789, 2045365, 3093941, 5191093, 7288245, 11482549, 15676853, 28259765, 24065461

Offset: 1

Antti Karttunen, Nov 16 2012

Antti Karttunen, Table of n, a(n) for n = 1..1024

Subset of A218614, i.e. a(n) = A218614(A005187(n)).

Also, a(n) = A054429(A218791(n)). Used to construct A218782, A218783. Cf. also A218787, A218788

a(n) = A218614(A005187(n)).

cp's OEIS Frontend

A218777 A014486-indices for the Beanstalk-tree growing one natural number at time, starting from the tree of one internal node (1), with the "lesser numbers to the left hand side" construction.

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A218779 A014486-indices for the Beanstalk-tree growing one natural number at time, starting from the tree of one internal node (1), with the "lesser numbers to the right hand side" construction.

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A218782 A014486-codes for the compact representation of Beanstalk-tree, growing by two natural numbers at time, starting from the tree of one internal node (1) and two leaves (3 and 2), with the larger numbers coming to the left hand side.

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Examples

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A218790 a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218782.

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Author

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Crossrefs

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