A199299 a(n) = (2*n + 1)*6^n.

1, 18, 180, 1512, 11664, 85536, 606528, 4199040, 28553472, 191476224, 1269789696, 8344332288, 54419558400, 352638738432, 2272560758784, 14575734521856, 93096626946048, 592433080565760, 3757718396731392, 23765029860409344, 149902496042582016, 943288877536247808

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-36).

Formula

a(n) = 12*a(n-1) - 36*a(n-2).

G.f.: (1+6*x)/(1-6*x)^2.

a(n) = 6*a(n-1) + 2*6^n. - Vincenzo Librandi, Nov 05 2011

From Amiram Eldar, Dec 10 2022: (Start)

Sum_{n>=0} 1/a(n) = sqrt(6)*arccoth(sqrt(6)).

Sum_{n>=0} (-1)^n/a(n) = sqrt(6)*arccot(sqrt(6)). (End)

E.g.f.: exp(6*x)*(1 + 12*x). - Stefano Spezia, May 07 2023

Mathematica

a[n_] := (2*n + 1)*6^n; Array[a, 25, 0] (* Amiram Eldar, Dec 10 2022 *)

Prog

(Magma) [(2*n+1)*6^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
(PARI) a(n) = (2*n+1)*6^n \\ Amiram Eldar, Dec 10 2022

Crossrefs

Cf. A014480, A058962, A124647, A155988, A171220, A199300, A199301.

Sequence in context: A341370 A004410 A140325 * A155669 A160954 A160955

Adjacent sequences: A199296 A199297 A199298 * A199300 A199301 A199302

Keyword

nonn,easy

Author

Philippe Deléham, Nov 04 2011

Status

approved