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A145978 Expansion of 1/(1-x*(1-8*x)). 7
1, 1, -7, -15, 41, 161, -167, -1455, -119, 11521, 12473, -79695, -179479, 458081, 1893913, -1770735, -16922039, -2756159, 132620153, 154669425, -906291799, -2143647199, 5106687193, 22255864785, -18597632759, -196644551039, -47863488967, 1525292919345 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-8).

FORMULA

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

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

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

MATHEMATICA

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

LinearRecurrence[{1, -8}, {1, 1}, 50] (* G. C. Greubel, Jan 29 2016 *)

PROG

(Sage) [lucas_number1(n, 1, 8) for n in xrange(1, 27)] # Zerinvary Lajos, Apr 22 2009

(PARI) Vec(1/(1-x*(1-8*x)) + O(x^40)) \\ Michel Marcus, Jan 29 2016

(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

CROSSREFS

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

Sequence in context: A048694 A041094 A042287 * A037376 A141548 A146159

Adjacent sequences:  A145975 A145976 A145977 * A145979 A145980 A145981

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Oct 26 2008

STATUS

approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)