A060242 a(n) = (2^n - 1)*(4^n - 1).

0, 3, 45, 441, 3825, 31713, 257985, 2080641, 16711425, 133955073, 1072692225, 8585738241, 68702695425, 549688696833, 4397778059265, 35183298314241, 281470681677825, 2251782633684993, 18014329789743105, 144114913197424641, 1152920405094170625

Offset: 0

Author

N. J. A. Sloane, Mar 22 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).

Crossrefs

Cf. A000225, A024036.

Programs

Magma

[(2^n-1)^2*(2^n+1): n in [0..40]]; // G. C. Greubel, Nov 05 2024

Maple

f:= gfun:-rectoproc({a(n) - 15*a(n-1) + 70*a(n-2) - 120*a(n-3) + 64*a(n-4) = 0, a(0) = 0, a(1)=3, a(2)=45, a(3)=441}, a(n), remember): map(f, [$0..20]); # Georg Fischer, Feb 19 2021

Mathematica

Table[(2^n-1)(4^n-1),{n,0,20}] (* Harvey P. Dale, May 13 2019 *)

PARI

a(n) = (2^n - 1)*(4^n - 1); \\ Harry J. Smith, Jul 04 2009

SageMath

def A060242(n): return (2^n-1)*(4^n-1)
[A060242(n) for n in range(41)] # G. C. Greubel, Nov 05 2024

Formula

G.f.: 3*x*(1-8*x^2)/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)). - Alois P. Heinz, Feb 19 2021

E.g.f.: exp(x) - exp(2*x) - exp(4*x) + exp(8*x). - G. C. Greubel, Nov 05 2024