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 A146080 Expansion of 1/(1-x*(1-10*x)). 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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). 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). a(n) = -(1/78)*i*(1/2 + (1/2)*i*sqrt(39))^n*sqrt(39) + (1/2)*(1/2 + (1/2)*i*sqrt(39))^n + (1/78)*i*sqrt(39)*(1/2 - (1/2)*i*sqrt(39))^n + (1/2)*(1/2 - (1/2)*i*sqrt(39))^n, with n>=0 and i=sqrt(-1). - Paolo P. Lava, Nov 18 2008 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 MAPLE a:=series(1/(1-x*(1-10*x)), x=0, 26): seq(coeff(a, x, n), n=0..25); # Paolo P. Lava, Mar 28 2019 MATHEMATICA Join[{a=1, b=1}, Table[c=b-10*a; a=b; b=c, {n, 80}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *) CoefficientList[Series[1/(1-x(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, -10}, {1, 1}, 30] (* Harvey P. Dale, Dec 16 2012 *) PROG (Sage) [lucas_number1(n, 1, 10) for n in xrange(1, 27)] # Zerinvary Lajos, Apr 22 2009 (PARI) Vec(1/(1-x*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012 (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 CROSSREFS Sequence in context: A146459 A308025 A041158 * A259093 A186508 A000981 Adjacent sequences:  A146077 A146078 A146079 * A146081 A146082 A146083 KEYWORD sign,easy AUTHOR Philippe Deléham, Oct 27 2008 STATUS approved

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)