A081337 - OEIS

%I #14 Jul 14 2023 15:30:13

%S 1,6,40,288,2176,16896,133120,1056768,8421376,67239936,537395200,

%T 4297064448,34368126976,274911461376,2199157473280,17592722915328,

%U 140739635838976,1125908496777216,9007233614479360,72057731476881408

%N a(n) = (8^n + 4^n)/2.

%C Binomial transform of A081336. 6th binomial transform of (1,0,4,0,16,0,64,....).

%H Vincenzo Librandi, <a href="/A081337/b081337.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-32).

%F a(n) = 12*a(n-1) -32*a(n-2), a(0)=1, a(1)=6.

%F G.f.: (1-6*x)/((1-4*x)*(1-8*x)).

%F E.g.f.: exp(6*x) * cosh(2*x).

%t CoefficientList[Series[(1 - 6 x) / ((1 - 4 x) (1 - 8 x)),{x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)

%o (Magma) [(8^n+4^n)/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 08 2013

%Y Cf. A081338.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Mar 18 2003