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A115968 Expansion of 1/(sqrt(1-4*x) + sqrt(1-2*x-3*x^2) - 1). 1

%I

%S 1,3,13,57,255,1149,5201,23607,107345,488721,2227007,10154511,

%T 46323507,211396611,964966149,4405717137,20118308687,91880092029,

%U 419657355725,1916914550859,8756654087981,40003289475363,182755724339143

%N Expansion of 1/(sqrt(1-4*x) + sqrt(1-2*x-3*x^2) - 1).

%H G. C. Greubel, <a href="/A115968/b115968.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: A(x)*B(x)/(A(x) +B(x) -A(x)*B(x)) where A(x) is the g.f. of A000984 and B(x) is the g.f. of A002426.

%t CoefficientList[Series[1/(Sqrt[1-4*x] +Sqrt[1-2*x-3*x^2] -1), {x, 0, 30} ], x] (* _G. C. Greubel_, Mar 08 2017 *)

%o (PARI) my(x='x+O('x^30)); Vec(1/(sqrt(1-4*x) + sqrt(1-2*x-3*x^2) - 1)) \\ _G. C. Greubel_, Mar 08 2017

%o (MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(Sqrt(1-4*x) + Sqrt(1-2*x-3*x^2) - 1) )); // _G. C. Greubel_, May 06 2019

%o (Sage) (1/(sqrt(1-4*x) + sqrt(1-2*x-3*x^2) - 1)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 06 2019

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 03 2006

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)