A271945 Expansion of 4*x^2/(1 - x - 9*x^2 + x^3).
0, 0, 4, 4, 40, 72, 428, 1036, 4816, 13712, 56020, 174612, 665080, 2180568, 7991676, 26951708, 96696224, 331269920, 1174584228, 4059317284, 14299305416, 49658576744, 174293008204, 606920893484, 2125899390576, 7413894423728, 25940068045428, 90539218468404
Offset: 0
Links
- Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3 (page 26, table 5).
- Index entries for linear recurrences with constant coefficients, signature (1,9,-1).
Programs
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Magma
[n le 2 select 2*n*(n-1) else Self(n)+9*Self(n-1)-Self(n-2): n in [0..30]];
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Mathematica
CoefficientList[Series[4 x^2 /(1 - x - 9 x^2 + x^3), {x, 0, 30}], x] LinearRecurrence[{1,9,-1},{0,0,4},30] (* Harvey P. Dale, Jul 18 2021 *) -
PARI
x='x+O('x^99); concat([0, 0], Vec(4*x^2/(1-x-9*x^2+x^3))) \\ Altug Alkan, Apr 18 2016 -
Sage
gf = 4*x^2/(1 - x - 9*x^2 + x^3); taylor(gf, x, 0, 30).list() # Bruno Berselli, Apr 18 2016
Formula
G.f.: 4*x^2/(1 - x - 9*x^2 + x^3).
a(n) = a(n-1) + 9*a(n-2) - a(n-3).