cp's OEIS Frontend

A134250 Expansion of x*(4+9*x-7*x^2) / ((1-x)*(1+3*x-x^2)).

%I A134250 #23 May 17 2017 04:25:32
%S A134250 4,1,7,-14,55,-173,580,-1907,6307,-20822,68779,-227153,750244,
%T A134250 -2477879,8183887,-27029534,89272495,-294847013,973813540,-3216287627,
%U A134250 10622676427,-35084316902,115875627139,-382711198313,1264009222084,-4174738864559,13788225815767
%N A134250 Expansion of x*(4+9*x-7*x^2) / ((1-x)*(1+3*x-x^2)).
%H A134250 Colin Barker, <a href="/A134250/b134250.txt">Table of n, a(n) for n = 1..1000</a>
%H A134250 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,4,-1).
%F A134250 a(n) = 2-17*(-1)^n*A006190(n) +5*(-1)^n*A006190(n+1). - _R. J. Mathar_, Dec 06 2011
%F A134250 From _Colin Barker_, May 16 2017: (Start)
%F A134250 a(n) = 2 + (2^(-1-n)*((-3-sqrt(13))^n*(-19+5*sqrt(13)) + (-3+sqrt(13))^n*(19+5*sqrt(13)))) / sqrt(13).
%F A134250 a(n) = -2*a(n-1) + 4*a(n-2) - a(n-3) for n>3.
%F A134250 (End)
%p A134250 A134250 := proc(n)
%p A134250         2-17*(-1)^n*A006190(n)+5*(-1)^n*A006190(n+1) ;
%p A134250 end proc:
%p A134250 seq(A134250(n),n=1..10) ; # _R. J. Mathar_, Dec 06 2011
%t A134250 LinearRecurrence[{-2,4,-1},{4,1,7},30] (* _Harvey P. Dale_, Aug 15 2015 *)
%t A134250 Rest@ CoefficientList[Series[x (4 + 9 x - 7 x^2)/((1 - x) (1 + 3 x - x^2)), {x, 0, 27}], x] (* _Michael De Vlieger_, May 16 2017 *)
%o A134250 (PARI) Vec(x*(4+9*x-7*x^2)/((1-x)*(1+3*x-x^2)) + O(x^30)) \\ _Colin Barker_, May 16 2017
%Y A134250 Cf. A062709, A052548.
%K A134250 easy,sign
%O A134250 1,1
%A A134250 _Roger L. Bagula_, Jan 14 2008