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

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

Author

Vincenzo Librandi, Jun 05 2015

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

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).

Programs

Magma

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

Mathematica

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 *)

Formula

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