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

1, 3, 13, 57, 255, 1149, 5201, 23607, 107345, 488721, 2227007, 10154511, 46323507, 211396611, 964966149, 4405717137, 20118308687, 91880092029, 419657355725, 1916914550859, 8756654087981, 40003289475363, 182755724339143

Offset

0,2

Links

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

Formula

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.

Mathematica

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 *)

Prog

(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
(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
(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

Crossrefs

Sequence in context: A010921 A275634 A163606 * A256939 A005827 A151319

Adjacent sequences: A115965 A115966 A115967 * A115969 A115970 A115971

Keyword

easy,nonn

Author

Paul Barry, Feb 03 2006

Status

approved