A230539 a(n) = 3*n*2^(3*n-1).

0, 12, 192, 2304, 24576, 245760, 2359296, 22020096, 201326592, 1811939328, 16106127360, 141733920768, 1236950581248, 10720238370816, 92358976733184, 791648371998720, 6755399441055744, 57420895248973824, 486388759756013568, 4107282860161892352

Offset: 0

Author

Bruno Berselli, Oct 23 2013

Keywords

• nonn
• easy

Comments

Arithmetic derivative of 8^n: a(n) = A003415(8^n).

Sum of reciprocals of a(n), for n>0: (2/3)*log(8/7).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (16,-64).

Crossrefs

Cf. A001018, A003415.

Cf. arithmetic derivative of k^n: A001787 (k=2), A027471 (k=3), A018215 (k=4), A053464 (k=5), A212700 (k=6), A027473 (k=7), this sequence, A230540 (k=9), A085708 (k=10), A081127 (k=11).

Row n=8 of A258997.

Programs

Magma

[3*n*2^(3*n-1): n in [0..20]];

Maple

A230539:=n->3*n*2^(3*n-1): seq(A230539(n), n=0..30); # Wesley Ivan Hurt, May 03 2017

Mathematica

Table[3 n 2^(3 n - 1), {n,0,20}]
LinearRecurrence[{16,-64},{0,12},20] (* Harvey P. Dale, Dec 25 2022 *)

PARI

a(n) = 3*n*2^(3*n-1); \\ Michel Marcus, Oct 23 2013

Formula

G.f.: 12*x/(1-8*x)^2.

a(n) = 12*A053539(n).