A171496 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 6, a(1) = 28.

6, 28, 120, 496, 2016, 8128, 32640, 130816, 523776, 2096128, 8386560, 33550336, 134209536, 536854528, 2147450880, 8589869056, 34359607296, 137438691328, 549755289600, 2199022206976, 8796090925056, 35184367894528

Offset: 0

Author

Klaus Brockhaus, Dec 10 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A171495; second binomial transform of A171494; third binomial transform of A010726.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Equals 2*A171499.

Cf. A171476, A006516, A010036, A171494, A171495, A010726, A171472, A171473.

Programs

Magma

[8*4^n-2*2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

Mathematica

LinearRecurrence[{6,-8},{6,28},30] (* Harvey P. Dale, Dec 21 2014 *)

PARI

{m=22; v=concat([6, 28], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 8*4^n - 2*2^n.

G.f.: 2*(3-4*x)/((1-2*x)*(1-4*x)).

a(n) = A171476(n+1) = A006516(n+2).

a(n+1) - a(n) = A010036(n+2).

a(n) = 4*a(n-1)+2^(n+1) (with a(0)=6). - Vincenzo Librandi, Dec 04 2010

E.g.f.: 2*exp(2*x)*(2*exp(2*x) - 1)*(2*exp(2*x) + 1). - Stefano Spezia, Dec 10 2021