A192877 Coefficient of x in the reduction by (x^2->x+1) of the polynomial p(n,x) given in Comments.

0, 1, 4, 14, 47, 152, 496, 1601, 5192, 16786, 54351, 175836, 569100, 1841513, 5959484, 19284934, 62407951, 201955408, 653543000, 2114907025, 6843987040, 22147600586, 71671151919, 231932702004, 750550018452, 2428830833977

Offset

0,3

Comments

The polynomial p(n,x) is defined by p(0,x) = 1, p(1,x) = x + 1, 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)*(1+x-x^2)*(1-2*x-4*x^2) ). - R. J. Mathar, May 06 2014

Mathematica

(See A192876.)
LinearRecurrence[{2, 6, -5, -6, 4}, {0, 1, 4, 14, 47}, 30] (* G. C. Greubel, Jan 08 2019 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+2*x)/((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)*(1+x-x^2)*(1-2*x-4*x^2)) )); // G. C. Greubel, Jan 08 2019
(Sage) (x*(1+2*x)/((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, 4, 14, 47];; 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, A192876.

Sequence in context: A326346 A046718 A291385 * A263622 A104487 A247210

Adjacent sequences: A192874 A192875 A192876 * A192878 A192879 A192880

Keyword

nonn

Author

Clark Kimberling, Jul 11 2011

Status

approved