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A145976 Expansion of 1/(1-x*(1-7*x)). 8

%I

%S 1,1,-6,-13,29,120,-83,-923,-342,6119,8513,-34320,-93911,146329,

%T 803706,-220597,-5846539,-4302360,36623413,66739933,-189623958,

%U -656803489,670564217,5268188640,574239121,-36303081359,-40322755206,213798814307

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

%C Row sums of Riordan array (1,x(1-7x)).

%H G. C. Greubel, <a href="/A145976/b145976.txt">Table of n, a(n) for n = 0..1500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, -7).

%F a(n) = a(n-1) - 7*a(n-2), a(0)=1, a(1)=1.

%F a(n) = Sum_{k=0..n} A109466(n,k)*7^(n-k).

%F a(n) = -(1/18)*i*sqrt(3)*(1/2 + (3/2)*i*sqrt(3))^n + (1/18)*i*sqrt(3)*(1/2 - (3/2)*i*sqrt(3))^n + (1/2)*(1/2 - (3/2)*i*sqrt(3))^n + (1/2)*(1/2 + (3/2)*i*sqrt(3))^n, with n >= 0 and i=sqrt(-1). - _Paolo P. Lava_, Nov 18 2008

%t Join[{a=1,b=1},Table[c=b-7*a;a=b;b=c,{n,80}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2011 *)

%t CoefficientList[Series[1/(1-x(1-7x)),{x,0,50}],x] (* or *) LinearRecurrence[{1,-7},{1,1},50] (* _Harvey P. Dale_, May 11 2011 *)

%o (Sage) [lucas_number1(n,1,7) for n in range(1, 29)] # _Zerinvary Lajos_, Apr 22 2009

%o (PARI) Vec(1/(1-x*(1-7*x)) + O(x^40)) \\ _Michel Marcus_, Jan 29 2016

%o (MAGMA) I:=[1,1]; [n le 2 select I[n] else Self(n-1) - 7*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 19 2018

%Y Cf. A010892, A107920, A106852, A106853, A106854, A145934.

%K sign,easy

%O 0,3

%A _Philippe Deléham_, Oct 26 2008

%E Corrected by _Zerinvary Lajos_, Apr 22 2009

%E Corrected by _D. S. McNeil_, Aug 20 2010

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Last modified September 20 19:17 EDT 2020. Contains 337265 sequences. (Running on oeis4.)