A005032 -id:A005032 - cp's OEIS frontend

A160798 a(n) = A160797(n+2)/3.

1, 7, 1, 7, 3, 21, 1, 7, 3, 21, 3, 21, 9, 63, 1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189, 1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189, 3, 21, 9, 63, 9, 63, 27, 189, 9, 63, 27, 189, 27, 189, 81, 567, 1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63

Offset: 1

Omar E. Pol, Jun 13 2009

From Omar E. Pol, Mar 15 2020: (Start)
It appears that the right border of triangle gives A005032.
It appears that the sum of n-th row equals A004171(n). (End)
Apparently A160417 shifted once left. - R. J. Mathar, May 30 2025

			From _Omar E. Pol_, Mar 15 2020: (Start)
Written as an irregular triangle in which row lengths are the even powers of 2, the sequence begins:
1, 7;
1, 7, 3, 21;
1, 7, 3, 21, 3, 21, 9, 63;
1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189;
1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189, 3, 21, 9, 63, 9, 63, ...
(End)

Cf. A004171, A005032, A160796, A160797.

More terms from Jinyuan Wang, Mar 15 2020

A166481 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.

Original entry on oeis.org

1, 7, 3, 21, 9, 63, 27, 189, 81, 567, 243, 1701, 729, 5103, 2187, 15309, 6561, 45927, 19683, 137781, 59049, 413343, 177147, 1240029, 531441, 3720087, 1594323, 11160261, 4782969, 33480783, 14348907, 100442349, 43046721, 301327047

Offset: 1

Klaus Brockhaus, Oct 14 2009

nonn

Interleaving of A000244 and A005032.

Seventh binomial transform is A153598.

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (0,3).

Cf. A000244 (powers of 3), A005032 (7*3^n), A153598.

[ n le 2 select 6*n-5 else 3*Self(n-2): n in [1..34] ];

LinearRecurrence[{0,3},{1,7},50] (* or *) Flatten[NestList[3#&,{1,7},20]] (* Harvey P. Dale, Sep 24 2015 *)

def A166481(n): return 3^(n/2)*(sqrt(3)*(n%2) + 7*((n+1)%2))/3
[A166481(n) for n in range(1,41)] # G. C. Greubel, Aug 02 2024

a(n) = (5 + 2*(-1)^n)*3^((2*n - 5 + (-1)^n)/4).
G.f.: x*(1+7*x)/(1-3*x^2).
E.g.f.: (1/3)*(-7 + 7*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - G. C. Greubel, Aug 02 2024

A258597 a(n) = 13*3^n.

Original entry on oeis.org

13, 39, 117, 351, 1053, 3159, 9477, 28431, 85293, 255879, 767637, 2302911, 6908733, 20726199, 62178597, 186535791, 559607373, 1678822119, 5036466357, 15109399071, 45328197213, 135984591639, 407953774917, 1223861324751, 3671583974253, 11014751922759

Offset: 0

Vincenzo Librandi, Jun 05 2015

Also maximum leaf number of the (n+3)-Apollonian network for n >= 0. - Eric W. Weisstein, Jan 17 2018

Eric Weisstein's World of Mathematics, Apollonian Network
Eric Weisstein's World of Mathematics, Maximum Leaf Number
Index entries for linear recurrences with constant coefficients, signature (3).

Cf. k*3^n: A000244 (k=1,3,9), A008776 (k=2,6), A003946 (k=4), A005030 (k=5), A005032 (k=7), A005051 (k=8), A005052 (k=10), A120354 (k=11), A003946 (k=12), this sequence (k=13), A258598 (k=17), A176413 (k=19).

Magma
```
[13*3^n: n in [0..30]];
```

Table[13 3^n, {n, 0, 30}]
13 3^Range[0, 20] (* Eric W. Weisstein, Jan 17 2018 *)
LinearRecurrence[{3}, {13}, 20] (* Eric W. Weisstein, Jan 17 2018 *)
CoefficientList[Series[13/(1 - 3 x), {x, 0, 20}], x] (* Eric W. Weisstein, Jan 17 2018 *)

G.f.: 13/(1-3*x).
a(n) = 3*a(n-1).
a(n) = 13*A000244(n).
E.g.f.: 13*exp(3*x). - Elmo R. Oliveira, Aug 16 2024

cp's OEIS Frontend

A160798 a(n) = A160797(n+2)/3.

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A166481 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.

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A258597 a(n) = 13*3^n.

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