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

0,3

Comments

For discussions of polynomial reduction, see A192232 and A192744.

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).

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

Mathematica

(See A192806.)
LinearRecurrence[{7, -5, 1}, {0, 1, 6}, 30] (* Harvey P. Dale, Oct 09 2017 *)

Prog

(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
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( 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
(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

Crossrefs

Cf. A192744, A192232, A192806, A099464.

Sequence in context: A255119 A005668 A018904 * A076026 A161734 A081570

Adjacent sequences: A192804 A192805 A192806 * A192808 A192809 A192810

Keyword

nonn,easy

Author

Clark Kimberling, Jul 10 2011

Status

approved