A192807 Coefficient of x in the reduction of the polynomial (x^2 + x + 1)^n by x^3 -> x^2 + x + 1.
0, 1, 6, 37, 230, 1431, 8904, 55403, 344732, 2145013, 13346834, 83047505, 516743378, 3215312955, 20006521300, 124485827703, 774583500376, 4819661885417, 29989201523742, 186600684739485, 1161078447443102, 7224534909928031
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-5,1).
Programs
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GAP
a:=[0,1,6];; for n in [4..25] do a[n]:=7*a[n-1]-5*a[n-2]+a[n-3]; od; Print(a); # Muniru A Asiru, Jan 02 2019
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(x-1)/(x^3-5*x^2+7*x-1) )); // G. C. Greubel, Jan 02 2019 -
Mathematica
(See A192806.) LinearRecurrence[{7,-5,1},{0,1,6},30] (* Harvey P. Dale, Oct 09 2017 *)
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PARI
my(x='x+O('x^30)); concat([0], Vec(x*(x-1)/(x^3-5*x^2+7*x-1))) \\ G. C. Greubel, Jan 02 2019 -
Sage
(x*(x-1)/(x^3-5*x^2+7*x-1)).series(x,30).coefficients(x, sparse=False) # G. C. Greubel, Jan 02 2019
Formula
a(n) = 7*a(n-1) - 5*a(n-2) + a(n-3).
G.f.: x*(x - 1)/(x^3 - 5*x^2 + 7*x - 1). - Colin Barker, Nov 23 2012
Comments