A146080 Expansion of 1/(1-x*(1-10*x)).

1, 1, -9, -19, 71, 261, -449, -3059, 1431, 32021, 17711, -302499, -479609, 2545381, 7341471, -18112339, -91527049, 89596341, 1004866831, 108903421, -9939764889, -11028799099, 88368849791, 198656840781, -685031657129, -2671600064939

Offset: 0

Author

Philippe Deléham, Oct 27 2008

Keywords

• sign
• easy

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-10).

Programs

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

Mathematica

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

PARI

Vec(1/(1-x*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012

Sage

[lucas_number1(n,1,10) for n in range(1, 27)] # Zerinvary Lajos, Apr 22 2009

Formula

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

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

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