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A192809
Coefficient of x in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.
3
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
0,3
COMMENTS
For discussions of polynomial reduction, see A192232 and A192744.
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
MATHEMATICA
(See A192808.)
LinearRecurrence[{7, -12, 8}, {0, 0, 2}, 30] (* G. C. Greubel, Jan 02 2019 *)
PROG
(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
(Magma) m:=30; R<x>:=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
(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
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 10 2011
STATUS
approved