A091629 -id:A091629 - cp's OEIS frontend

A191566 a(n) = 7a(n-1) + (-1)^n6*2^(n-1).

1, 1, 19, 109, 811, 5581, 39259, 274429, 1921771, 13450861, 94159099, 659107549, 4613765131, 32296331341, 226074368539, 1582520481469, 11077643566891, 77543504575021, 542804532811579, 3799631728108189

Offset: 0

Paul Curtz, Jun 06 2011

A007283(n) = 3*2^n. A091629(n+1) = 6*2^n.
a(n) + a(n+2) = 10 * (b(n) = 2, 11, 83, 569, 4007, ...).
b(n+1) = 7*b(n) - (-1)^n*3*2^n.
Inverse binomial transform of A007613(n).

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (5,14).

[(7^n+2*(-2)^n)/3: n in [0..30]]; // Vincenzo Librandi, Jun 07 2011

LinearRecurrence[{5,14},{1,1},40] (* Harvey P. Dale, Mar 01 2017 *)
CoefficientList[Series[(1 - 4*x)/(1 - 5*x - 14*x^2), {x, 0, 20}], x] (* Stefano Spezia, Sep 12 2018 *)

a(n)=(7^n+2*(-2)^n)/3 \\ Charles R Greathouse IV, Jun 06 2011

a(n+1) - a(n) = 18 * (0 followed by A053573(n)).
a(n) = (7^n + 2*(-2)^n)/3. - Charles R Greathouse IV, Jun 06 2011
G.f.: (1-4*x)/(1 - 5*x - 14*x^2). - Bruno Berselli, Jun 07 2011
a(n) = 5*a(n-1) + 14*a(n-2).

A299962 Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the k-th positive number whose Collatz sequence contains n.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 6, 4, 4, 3, 4, 12, 5, 5, 6, 5, 5, 24, 6, 6, 7, 12, 6, 6, 48, 7, 7, 3, 9, 24, 7, 7, 96, 8, 8, 9, 5, 14, 48, 9, 8, 192, 9, 9, 3, 18, 6, 18, 96, 10, 9, 384, 10, 10, 7, 6, 36, 7, 28, 192, 11, 10, 768, 11, 11, 12, 9, 7, 72, 8, 36, 384, 12, 11

Offset: 1

Rémy Sigrist, Feb 22 2018

The n-th row corresponds to indices of rows in A070165 containing n.

			Array T(n, k) begins:
  n\k|  1     2     3     4     5     6     7     8     9    10
  ---+---------------------------------------------------------
    1|  1     2     3     4     5     6     7     8     9    10  -->  A000027 ?
    2|  2     3     4     5     6     7     8     9    10    11
    3|  3     6    12    24    48    96   192   384   768  1536  -->  A007283
    4|  3     4     5     6     7     8     9    10    11    12
    5|  3     5     6     7     9    10    11    12    13    14
    6|  6    12    24    48    96   192   384   768  1536  3072  -->  A091629
    7|  7     9    14    18    28    36    37    43    49    56
    8|  3     5     6     7     8     9    10    11    12    13
    9|  9    18    36    72   144   288   576  1152  2304  4608
   10|  3     6     7     9    10    11    12    13    14    15

Rémy Sigrist, PARI program for A299962
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A000027, A007283, A091629, A070165, A070167.

PARI
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See Links section.
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T(n, 1) = A070167(n) for any n > 0.
T(3*n, k) = 3*n * 2^(k-1) for any n > 0 and k > 0.
If the Collatz conjecture is true, then:
- T(1, k) = k for any k > 0,
- T(2, k) = k+1 for any k > 0.

cp's OEIS Frontend

A191566 a(n) = 7a(n-1) + (-1)^n6*2^(n-1).

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A299962 Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the k-th positive number whose Collatz sequence contains n.

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cp's OEIS Frontend

A191566 a(n) = 7*a(n-1) + (-1)^n*6*2^(n-1).

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

PARI

Formula

A299962 Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the k-th positive number whose Collatz sequence contains n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A191566 a(n) = 7a(n-1) + (-1)^n6*2^(n-1).