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Expansion of 1/(1 - x*(1 - 11*x)).
4

%I #54 Mar 08 2024 01:12:19

%S 1,1,-10,-21,89,320,-659,-4179,3070,49039,15269,-524160,-692119,

%T 5073641,12686950,-43123101,-182679551,291674560,2301149621,

%U -907270539,-26219916370,-16239940441,272179139629,450818484480,-2543152051439

%N Expansion of 1/(1 - x*(1 - 11*x)).

%C Row sums of Riordan array (1,x(1-11x)).

%H G. C. Greubel, <a href="/A146083/b146083.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,-11).

%F a(n) = a(n-1)-11*a(n-2) ; a(0)=1, a(1)=1.

%F a(n) = Sum_{k=0..n} A109466(n,k)*11^(n-k).

%F From _G. C. Greubel_, Jan 31 2016: (Start)

%F G.f.: 1/(1-x+11*x^2).

%F E.g.f.: exp(x/2)*(cos(sqrt(43)*x/2) + (1/sqrt(43))*sin(sqrt(43)*x/2)).

%F (End)

%t LinearRecurrence[{1,-11},{1,1},30] (* _Harvey P. Dale_, Jan 07 2016 *)

%o (Sage) [lucas_number1(n,1,11) for n in range(1, 26)] # _Zerinvary Lajos_, Apr 22 2009

%o (PARI) Vec(1/(1-x*(1-11*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (Magma) [n le 2 select 1 else Self(n-1)-11*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jan 31 2016

%Y Cf. A010892, A107920, A106852, A106853, A106854, A145934, A145976, A145978, A146078, A146080.

%K sign,easy

%O 0,3

%A _Philippe Deléham_, Oct 27 2008