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A145978 Expansion of 1/(1-x*(1-8*x)). 7

%I

%S 1,1,-7,-15,41,161,-167,-1455,-119,11521,12473,-79695,-179479,458081,

%T 1893913,-1770735,-16922039,-2756159,132620153,154669425,-906291799,

%U -2143647199,5106687193,22255864785,-18597632759,-196644551039,-47863488967,1525292919345

%N Expansion of 1/(1-x*(1-8*x)).

%C Row sums of Riordan array (1,1(1-8x)).

%H G. C. Greubel, <a href="/A145978/b145978.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,-8).

%F a(n) = a(n-1) - 8*a(n-2), a(0)=1, a(1)=1.

%F a(n) = Sum_{k=0..n} A109466(n,k)*8^(n-k).

%F a(n) = -(1/62)*i*(1/2 + (1/2)*i*sqrt(31))^n*sqrt(31) + (1/2)*(1/2 + (1/2)*i*sqrt(31))^n + (1/2)*(1/2 - (1/2)*i*sqrt(31))^n + (1/62)*i*(1/2 - (1/2)*i*sqrt(31))^n*sqrt(31), with i=sqrt(-1). - _Paolo P. Lava_, Nov 18 2008

%t Join[{a=1,b=1},Table[c=b-8*a;a=b;b=c,{n,80}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2011*)

%t LinearRecurrence[{1,-8},{1,1},50] (* _G. C. Greubel_, Jan 29 2016 *)

%o (Sage) [lucas_number1(n,1,8) for n in xrange(1, 27)] # _Zerinvary Lajos_, Apr 22 2009

%o (PARI) Vec(1/(1-x*(1-8*x)) + O(x^40)) \\ _Michel Marcus_, Jan 29 2016

%o (MAGMA) I:=[1,1]; [n le 2 select I[n] else Self(n-1) - 8*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 19 2018

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

%K sign,easy

%O 0,3

%A _Philippe Deléham_, Oct 26 2008

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Last modified February 15 20:49 EST 2019. Contains 320138 sequences. (Running on oeis4.)