A059409 a(n) = 4^n * (2^n - 1).

0, 4, 48, 448, 3840, 31744, 258048, 2080768, 16711680, 133955584, 1072693248, 8585740288, 68702699520, 549688705024, 4397778075648, 35183298347008, 281470681743360, 2251782633816064, 18014329790005248, 144114913197948928, 1152920405095219200

Offset: 0

Author

N. J. A. Sloane, Alford Arnold, Jan 30 2001

Keywords

• nonn
• easy

Comments

Jordan's totient functions are described more fully in A059379 and A059380; for example, J_1(n) is Euler's totient function and J_2(n) the Moebius transform of squares.

Examples

			(4,48,448,3840,...) = (8,64,512,4096,...) - (2,12,56,240,...) - (1,3,7,15,...) - (1,1,1,1,...)
		

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (12,-32).

Crossrefs

Cf. A059379, A059380, A016152.

Cf. A024023, A000225, A000012.

Cf. A065442.

Programs

GAP

List([0..100], n->4^n * (2^n - 1)); # Muniru A Asiru, Jan 29 2018

Magma

[4^n*(2^n - 1): n in [0..40]]; // Vincenzo Librandi, Apr 26 2011

Maple

seq(4^n * (2^n - 1), n=0..20); # Muniru A Asiru, Jan 29 2018

Mathematica

Table[4^n*(2^n - 1), {n,0,30}] (* G. C. Greubel, Jan 29 2018 *)
LinearRecurrence[{12,-32},{0,4},20] (* Harvey P. Dale, Oct 14 2019 *)

PARI

a(n) = { 4^n*(2^n - 1) } \\ Harry J. Smith, Jun 26 2009

Formula

Equals J_n(8) (see A059379).

J_n(8) = 8^n - A024023(n) - A000225(n) - A000012(n).

a(n) = 4*A016152(n).

G.f.: 4*x / ( (8*x-1)*(4*x-1) ). - R. J. Mathar, Nov 23 2018

Sum_{n>0} 1/a(n) = E - 4/3, where E is the Erdős-Borwein constant (A065442). - Peter McNair, Dec 19 2022

a(n) = A291779(A008585(n)) = A045991(A000079(n)). - Mathew Englander, Feb 08 2024