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A192875 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments. 3
0, 1, 3, 11, 37, 119, 391, 1257, 4087, 13195, 42757, 138271, 447615, 1448249, 4687071, 15166963, 49082501, 158832391, 513995543, 1663319433, 5382623015, 17418520571, 56367538373, 182409150671, 590288468367, 1910213517529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The polynomial p(n,x) is defined by p(0,x) = 1, p(1,x) = x, and p(n,x) = x*p(n-1,x) + 2*(x^2)*p(n-1,x) + 1.  See A192872.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,6,-5,-6,4).

FORMULA

a(n) = 2*a(n-1) + 6*a(n-2) - 5*a(n-3) - 6*a(n-4) + 4*a(n-5).

G.f.: x*(1+2*x)*(1-x+x^2) / ( (1-x)*(1+x-x^2)*(1-2*x-4*x^2)). - R. J. Mathar, May 06 2014

MAPLE

seq(coeff(series(x*(1+2*x)*(1-x+x^2)/((1-x)*(1+x-x^2)*(1-2*x-4*x^2)), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Jan 08 2019

MATHEMATICA

(See A192874.)

LinearRecurrence[{2, 6, -5, -6, 4}, {0, 1, 3, 11, 37}, 30] (* G. C. Greubel, Jan 08 2019 *)

PROG

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+2*x)*(1-x+x^2)/((1-x)*(1+ x-x^2)*(1-2*x-4*x^2)))) \\ G. C. Greubel, Jan 08 2019

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1+2*x)*(1-x+x^2)/((1-x)*(1+ x-x^2)*(1-2*x-4*x^2)) )); // G. C. Greubel, Jan 08 2019

(Sage) (x*(1+2*x)*(1-x+x^2)/((1-x)*(1+ x-x^2)*(1-2*x-4*x^2))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Jan 08 2019

(GAP) a:=[0, 1, 3, 11, 37];; for n in [6..30] do a[n]:=2*a[n-1]+6*a[n-2] - 5*a[n-3]-6*a[n-4]+4*a[n-5]; od; a; # G. C. Greubel, Jan 08 2019

CROSSREFS

Cf. A192872, A192874.

Sequence in context: A007615 A065540 A084171 * A118044 A027062 A134757

Adjacent sequences:  A192872 A192873 A192874 * A192876 A192877 A192878

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 11 2011

STATUS

approved

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Last modified June 5 11:52 EDT 2020. Contains 334840 sequences. (Running on oeis4.)