A036294 a(n) = n*8^n.

0, 8, 128, 1536, 16384, 163840, 1572864, 14680064, 134217728, 1207959552, 10737418240, 94489280512, 824633720832, 7146825580544, 61572651155456, 527765581332480, 4503599627370496, 38280596832649216, 324259173170675712, 2738188573441261568, 23058430092136939520

Offset: 0

Author

N. J. A. Sloane

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, A053539.

Programs

Magma

[n*8^n: n in [0..20]]; // Vincenzo Librandi, Aug 09 2017

Mathematica

Table[n 7^n, {n, 0, 30}] (* or *) LinearRecurrence[{16,-64},{0,8},31] (* Vincenzo Librandi, Aug 09 2017 *)

Formula

From Vincenzo Librandi, Aug 09 2017: (Start)

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

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

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = log(8/7).

Sum_{n>=1} (-1)^(n+1)/a(n) = log(9/8). (End)

From Elmo R. Oliveira, Sep 09 2024: (Start)

E.g.f.: 8*x*exp(8*x).

a(n) = n*A001018(n) = 8*A053539(n). (End)