A081626 - OEIS

%I #15 Sep 08 2022 08:45:09

%S 1,8,56,368,2336,14528,89216,543488,3293696,19893248,119883776,

%T 721399808,4336787456,26054279168,156459892736,939296227328,

%U 5637924847616,33836139020288,203051193860096,1218444602114048

%N 2*6^n-4^n.

%C Binomial transform of A081625. Inverse binomial transform of A081627.

%H Vincenzo Librandi, <a href="/A081626/b081626.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-24).

%F a(n) = 10*a(n-1)-24*a(n-2), a(0)=1, a(1)=8.

%F G.f.: (1-2*x)/((1-4*x)(1-6*x)).

%F E.g.f. 2*exp(6*x)-exp(4*x).

%t Table[2 6^n - 4^n, {n, 0, 20}] (* or *) LinearRecurrence[{10, -24}, {1, 8}, 20] (* _Harvey P. Dale_, Aug 19 2012 *)

%t CoefficientList[Series[(1 - 2 x) / ((1 - 4 x) (1 - 6 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)

%o (Magma) [2*6^n-4^n: n in [0..25]]; // _Vincenzo Librandi_, Aug 09 2013

%o (PARI) a(n)=2*6^n-4^n \\ _Charles R Greathouse IV_, Oct 07 2015

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 25 2003