A016130 - OEIS

%I #33 Sep 08 2022 08:44:40

%S 1,9,67,477,3355,23517,164683,1152909,8070619,56494845,395464939,

%T 2768256621,19377800443,135644611293,949512295435,6646586100813,

%U 46526102771227,325682719529661,2279779036969771

%N Expansion of 1/((1-2x)(1-7x)).

%H Vincenzo Librandi, <a href="/A016130/b016130.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 (9,-14)

%F a(n) = (7^(n+1) - 2^(n+1))/5. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 06 2005

%F a(n) = 7*a(n-1) + 2^n, a(0)=1. - _Vincenzo Librandi_, Jun 24 2013

%e 1/((1-2x)(1-7x)) = 1 + 9*x + 67*x^2 + 477*x^3 + 3355*x^4 + 23517*x^5 + 164683*x^6 + ...

%t Join[{a=1,b=9},Table[c=9*b-14*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)

%t CoefficientList[Series[1 /((1 - 2 x) (1 - 7 x)), {x, 0, 200}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)

%o (Sage) [lucas_number1(n,9,14) for n in range(1, 20)] # _Zerinvary Lajos_, Apr 23 2009

%o (Sage) [(7^n - 2^n)/5 for n in range(1,20)] # _Zerinvary Lajos_, Jun 04 2009

%o (PARI) Vec(1/((1-2*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x) (1-7*x)))); // _Vincenzo Librandi_, Jun 24 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_