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A126068 Expansion of 1 - x - sqrt(1 - 2*x - 3*x^2) in powers of x. 3
0, 0, 2, 2, 4, 8, 18, 42, 102, 254, 646, 1670, 4376, 11596, 31022, 83670, 227268, 621144, 1706934, 4713558, 13072764, 36398568, 101704038, 285095118, 801526446, 2259520830, 6385455594, 18086805002, 51339636952, 146015545604 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Except for initial terms, identical to A007971.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1 - x - sqrt(1 - 2*x - 3*x^2). - Michael Somos, Jan 25 2014

0 = a(n) * (9*a(n+1) + 15*a(n+2) - 12*a(n+3)) + a(n+1) * (-3*a(n+1) + 10*a(n+2) - 5*a(n+3)) + a(n+2) * (a(n+2) + a(n+3)) if n>0. - Michael Somos, Jan 25 2014

a(n) ~ 3^(n-1/2)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 20 2014

EXAMPLE

G.f. = 2*x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 18*x^6 + 42*x^7 + 102*x^8 + 254*x^9 + ...

MAPLE

zl:=4*(1-z+sqrt(1-2*z-3*z^2))/(1-z+sqrt(1-2*z-3*z^2))^2: gser:=series(zl, z=0, 35): seq(coeff(gser, z, n), n=-2..27);

MATHEMATICA

a[ n_] := SeriesCoefficient[ 1 - x - Sqrt[1 - 2 x - 3 x^2], {x, 0, n}]; (* Michael Somos, Jan 25 2014 *)

CoefficientList[Series[1 - x - Sqrt[1 - 2 x - 3 x^2], {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2014 *)

PROG

(PARI) {a(n) = polcoeff( (1 - x - sqrt(1 - 2*x - 3*x^2 + x * O(x^n))), n)}; /* Michael Somos, Jan 25 2014 */

CROSSREFS

Cf. A007971.

Sequence in context: A007971 * A167022 A168055 A005702 A095335 A283117

Adjacent sequences:  A126065 A126066 A126067 * A126069 A126070 A126071

KEYWORD

nonn

AUTHOR

Zerinvary Lajos, Feb 28 2007

EXTENSIONS

Better name by Michael Somos, Jan 25 2014

STATUS

approved

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Last modified October 22 02:46 EDT 2018. Contains 316431 sequences. (Running on oeis4.)