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

%I A171496 #23 Sep 08 2022 08:45:50
%S A171496 6,28,120,496,2016,8128,32640,130816,523776,2096128,8386560,33550336,
%T A171496 134209536,536854528,2147450880,8589869056,34359607296,137438691328,
%U A171496 549755289600,2199022206976,8796090925056,35184367894528
%N A171496 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 6, a(1) = 28.
%C A171496 Binomial transform of A171495; second binomial transform of A171494; third binomial transform of A010726.
%H A171496 Vincenzo Librandi, <a href="/A171496/b171496.txt">Table of n, a(n) for n = 0..500</a>
%H A171496 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).
%F A171496 a(n) = 8*4^n - 2*2^n.
%F A171496 G.f.: 2*(3-4*x)/((1-2*x)*(1-4*x)).
%F A171496 a(n) = A171476(n+1) = A006516(n+2).
%F A171496 a(n+1) - a(n) = A010036(n+2).
%F A171496 a(n) = 4*a(n-1)+2^(n+1) (with a(0)=6). - _Vincenzo Librandi_, Dec 04 2010
%F A171496 E.g.f.: 2*exp(2*x)*(2*exp(2*x) - 1)*(2*exp(2*x) + 1). - _Stefano Spezia_, Dec 10 2021
%t A171496 LinearRecurrence[{6,-8},{6,28},30] (* _Harvey P. Dale_, Dec 21 2014 *)
%o A171496 (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}
%o A171496 (Magma) [8*4^n-2*2^n: n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2011
%Y A171496 Equals 2*A171499.
%Y A171496 Cf. A171476, A006516, A010036, A171494, A171495, A010726, A171472, A171473.
%K A171496 nonn,easy
%O A171496 0,1
%A A171496 _Klaus Brockhaus_, Dec 10 2009