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A235800 Length of n-th vertical line segment from left to right in a diagram of a two-dimensional version of the Collatz (or 3x + 1) problem. 3
3, 1, 7, 2, 11, 3, 15, 4, 19, 5, 23, 6, 27, 7, 31, 8, 35, 9, 39, 10, 43, 11, 47, 12, 51, 13, 55, 14, 59, 15, 63, 16, 67, 17, 71, 18, 75, 19, 79, 20, 83, 21, 87, 22, 91, 23, 95, 24, 99, 25, 103, 26, 107, 27, 111, 28, 115, 29, 119, 30, 123, 31, 127, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In the diagram every cycle is represented by a directed graph.

After (3x + 1) the next step is (3y + 1).

After (x/2) the next step is (y/2).

A235801(n) gives the length of n-th horizontal line segment in the same diagram.

Also A004767 and A000027 interleaved.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

a(n) = A006370(n) - A193356(n).

From Chai Wah Wu, Sep 26 2016: (Start)

a(n) = 2*a(n-2) - a(n-4) for n > 4.

G.f.: x*(x^2 + x + 3)/((x - 1)^2*(x + 1)^2). (End)

EXAMPLE

The first part of the diagram in the first quadrant:

. . . . . . . . . . . . . . . . . . . . . . . .

.              _ _|_ _|_ _|_ _|_ _|_ _|_ _|_ _.

.             |   |   |   |   |   |   |   |_|_.

.             |   |   |   |   |   |   |  _ _|_.

.             |   |   |   |   |   |   |_|_ _|_.

.             |   |   |   |   |   |  _ _|_ _|_.

.             |   |   |   |   |   |_|_ _|_ _|_.

.          _ _|_ _|_ _|_ _|_ _|_ _ _|_ _|_ _|_.

.         |   |   |   |   |   |_|_ _|_ _|_ _|_.

.         |   |   |   |   |  _ _|_ _|_ _|_ _|_.

.         |   |   |   |   |_|_ _|_ _|_ _|_ _|_.

.         |   |   |   |  _ _|_ _|_ _|_ _|_ _|_.

.         |   |   |   |_|_ _|_ _|_ _|_ _|_ _| .

.      _ _|_ _|_ _|_ _ _|_ _|_ _|_ _|_ _|     .

.     |   |   |   |_|_ _|_ _|_ _|_ _|         .

.     |   |   |  _ _|_ _|_ _|_ _|             .

.     |   |   |_|_ _|_ _|_ _|                 .

.     |   |  _ _|_ _|_ _|                     .

.     |   |_|_ _|_ _|                         .

.  _ _|_ _ _|_ _|                             .

. |   |_|_ _|                                 .

. |  _ _|                                     .

. |_|                                         .

. . . . . . . . . . . . . . . . . . . . . . . .

. 3,1,7,2,11...

MATHEMATICA

LinearRecurrence[{0, 2, 0, -1}, {3, 1, 7, 2}, 70] (* Harvey P. Dale, Sep 29 2016 *)

PROG

(Python)

from __future__ import division

A235800_list = [4*(n//2) + 3 if n % 2 else n//2 for n in range(1, 10**4)] # Chai Wah Wu, Sep 26 2016

CROSSREFS

Cf. A000027, A004767, A005408, A006370, A014682, A016957, A070165, A193356, A235795, A235801.

Sequence in context: A065287 A065263 A057114 * A065259 A065289 A065265

Adjacent sequences:  A235797 A235798 A235799 * A235801 A235802 A235803

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 15 2014

STATUS

approved

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Last modified February 23 00:18 EST 2019. Contains 320411 sequences. (Running on oeis4.)