A199301 a(n) = (2n+1)*8^n.

1, 24, 320, 3584, 36864, 360448, 3407872, 31457280, 285212672, 2550136832, 22548578304, 197568495616, 1717986918400, 14843406974976, 127543348822016, 1090715534753792, 9288674231451648, 78812993478983680, 666532744850833408, 5620492334958379008, 47269781688880726016

Offset: 0

Author

Philippe Deléham, Nov 04 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16,-64).

Crossrefs

Cf. A001018 (Powers of 8), A005408 (2n+1).

Cf. A014480, A058962, A124647, A155988, A171220, A199299, A199300.

Programs

Magma

[(2*n+1)*8^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011

Maple

A199301:=n->(2*n+1)*8^n: seq(A199301(n), n=0..20); # Wesley Ivan Hurt, Oct 30 2014

Mathematica

Table[(2 n + 1)*8^n, {n, 0, 20}] (* Wesley Ivan Hurt, Oct 30 2014 *)

PARI

a(n) = (2*n+1)*8^n \\ Amiram Eldar, Dec 10 2022

Formula

a(n) = 16*a(n-1)-64*a(n-2).

G.f.: (1+8*x)/(1-8*x)^2.

a(n) = 8*(a(n-1)+2^(3*n-2)). - Vincenzo Librandi, Nov 05 2011

a(n) = A005408(n) * A001018(n). - Wesley Ivan Hurt, Oct 30 2014

From Amiram Eldar, Dec 10 2022: (Start)

Sum_{n>=0} 1/a(n) = sqrt(8)*arccoth(sqrt(8)).

Sum_{n>=0} (-1)^n/a(n) = sqrt(8)*arccot(sqrt(8)). (End)

E.g.f.: exp(8*x)*(1 + 16*x). - Stefano Spezia, May 09 2023

Extensions

a(18) corrected by Vincenzo Librandi, Nov 05 2011