A081657 - OEIS

%I #21 Sep 08 2022 08:45:09

%S 1,11,89,659,4721,33371,234569,1644899,11523041,80687531,564891449,

%T 3954476339,27682042961,193776426491,1356441362729,9495108670979,

%U 66465818092481,465260898834251,3256826808400409,22797789208484819

%N 2*7^n-3^n.

%C Binomial transform of A081656.

%H Vincenzo Librandi, <a href="/A081657/b081657.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,-21).

%F G.f.: (1+x)/((1-7*x)*(1-3*x)).

%F E.g.f. 2*exp(7*x)-exp(3*x).

%F a(0)=0, a(1)=11; for n>1, a(n) = 10*a(n-1) -21*a(n-2). - _Vincenzo Librandi_ Aug 10 2013

%t CoefficientList[Series[(1 + x) / ((1 - 7 x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 10 2013 *)

%o (Magma) [2*7^n-3^n: n in [0..30]]; // _Vincenzo Librandi_, Dec 05 2012

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 26 2003