login
Expansion of 1/(1-x*(1-10*x)).
6

%I #47 Mar 05 2024 11:25:48

%S 1,1,-9,-19,71,261,-449,-3059,1431,32021,17711,-302499,-479609,

%T 2545381,7341471,-18112339,-91527049,89596341,1004866831,108903421,

%U -9939764889,-11028799099,88368849791,198656840781,-685031657129,-2671600064939

%N Expansion of 1/(1-x*(1-10*x)).

%C Row sums of Riordan array (1,x(1-10x)).

%H G. C. Greubel, <a href="/A146080/b146080.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 (1,-10).

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

%F a(n) = Sum_{k=0..n} A109466(n,k)*10^(n-k).

%F E.g.f.: exp(x/2)*(cos(sqrt(39)*x/2) + (1/sqrt(39))*sin(sqrt(39)*x/2)). - _G. C. Greubel_, Jan 30 2016

%t CoefficientList[Series[1/(1-x(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{1,-10},{1,1},30] (* _Harvey P. Dale_, Dec 16 2012 *)

%o (Sage) [lucas_number1(n,1,10) for n in range(1, 27)] # _Zerinvary Lajos_, Apr 22 2009

%o (PARI) Vec(1/(1-x*(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Jan 12 2012

%o (Magma) I:=[1,1]; [n le 2 select I[n] else Self(n-1) - 10*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 19 2018

%K sign,easy

%O 0,3

%A _Philippe Deléham_, Oct 27 2008