A192809 Coefficient of x in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.

0, 0, 2, 14, 74, 366, 1786, 8702, 42410, 206734, 1007834, 4913310, 23953034, 116774190, 569289402, 2775359806, 13530239338, 65961672910, 321571716762, 1567703857118, 7642759781962, 37259445922414, 181644634930298, 885541171698814

Offset: 0

Author

Clark Kimberling, Jul 10 2011

Keywords

• nonn
• easy

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,-12,8).

Crossrefs

Cf. A192744, A192232, A192808, A192811.

Programs

GAP

a:=[0,0,2];; for n in [4..25] do a[n]:=7*a[n-1]-12*a[n-2]+8*a[n-3]; od; Print(a); # Muniru A Asiru, Jan 02 2019

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!( 2*x^2/(1-7*x+12*x^2-8*x^3) )); // G. C. Greubel, Jan 02 2019

Mathematica

(See A192808.)
LinearRecurrence[{7,-12,8}, {0,0,2}, 30] (* G. C. Greubel, Jan 02 2019 *)

PARI

my(x='x+O('x^30)); concat([0,0], Vec(2*x^2/(1-7*x+12*x^2-8*x^3))) \\ G. C. Greubel, Jan 02 2019

Sage

(2*x^2/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 02 2019

Formula

a(n) = 7*a(n-1) - 12*a(n-2) + 8*a(n-3).

a(n) = 2*A192811(n).

G.f.: 2*x^2/(1-7*x+12*x^2-8*x^3). - Colin Barker, Jul 26 2012