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%I #17 Sep 08 2022 08:45:09
%S 1,10,68,424,2576,15520,93248,559744,3358976,20154880,120931328,
%T 725592064,4353560576,26121379840,156728311808,940369936384,
%U 5642219749376,33853318758400,203119913074688,1218719479496704
%N 2*6^n-2^n.
%C Binomial transform of A081655. Inverse binomial transform of A081657.
%H Vincenzo Librandi, <a href="/A081656/b081656.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (8,-12).
%F G.f.: (1+2*x)/((1-6*x)(1-2*x)).
%F E.g.f. 2exp(6*x)-exp(2*x).
%F a(0)=1, a(2)=10; for n>2, a(n) = 8*a(n-1) -12*a(n-2). - _Vincenzo Librandi_, Aug 10 2013
%t CoefficientList[Series[(1 + 2 x) / ((1 - 6 x) (1 - 2 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 10 2013 *)
%t Table[2*6^n-2^n,{n,0,20}] (* or *) LinearRecurrence[{8,-12},{1,10},20] (* _Harvey P. Dale_, Mar 17 2019 *)
%o (Magma) [2*6^n-2^n: n in [0..30]]; // _Vincenzo Librandi_, Aug 10 2013
%o (PARI) a(n)=2*6^n-2^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Third column of array A094424.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 26 2003
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