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A126068
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Expansion of 1 - x - sqrt(1 - 2*x - 3*x^2) in powers of x.
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3
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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
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OFFSET
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0,3
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COMMENTS
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Except for initial terms, identical to A007971.
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LINKS
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FORMULA
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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
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EXAMPLE
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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 + ...
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MAPLE
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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);
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MATHEMATICA
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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 *)
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PROG
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(PARI) {a(n) = polcoeff( (1 - x - sqrt(1 - 2*x - 3*x^2 + x * O(x^n))), n)}; /* Michael Somos, Jan 25 2014 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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