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a(n) = (2*8^n + 2^n)/3.
8

%I #18 Sep 30 2018 13:22:42

%S 1,6,44,344,2736,21856,174784,1398144,11184896,89478656,715828224,

%T 5726623744,45812985856,366503878656,2932031012864,23456248070144,

%U 187649984495616,1501199875833856,12009599006408704,96076792050745344,768614336404914176

%N a(n) = (2*8^n + 2^n)/3.

%C Binomial transform of A083076.

%H Nathaniel Johnston, <a href="/A082412/b082412.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).

%F G.f.: (1-4*x)/((1-2*x)*(1-8*x));

%F E.g.f.: (2*exp(8*x) + exp(2*x))/3.

%F a(n) = (2*8^n + 2^n)/3.

%F a(n) = 2^n*A001045(2n+1). - _Paul Barry_, Sep 10 2007

%p seq((2*8^n+2^n)/3,n=0..20); # _Nathaniel Johnston_, Jun 26 2011

%t Table[(2*8^n+2^n)/3,{n,0,30}] (* or *) LinearRecurrence[{10,-16},{1,6},30] (* _Harvey P. Dale_, Sep 30 2018 *)

%o (PARI) a(n)=(2*8^n+2^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A082413.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 23 2003