A192905 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.

0, 1, 3, 8, 25, 79, 248, 777, 2435, 7632, 23921, 74975, 234992, 736529, 2308483, 7235416, 22677769, 71078319, 222778856, 698249753, 2188505347, 6859373216, 21499148257, 67384199871, 211200478176, 661959956001, 2074763216131

Offset

0,3

Comments

The titular polynomial is defined by p(n,x) = (x^2)*p(n-1,x) + x*p(n-2,x), with p(0,x) = 1, p(1,x) = x. For details, see A192904.

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,0,1,1).

Formula

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

G.f.: x*(1-x)*(1+x)/(1-3*x-x^3-x^4). - Colin Barker, Aug 31 2012

Mathematica

(See A192904.)
LinearRecurrence[{3, 0, 1, 1}, {0, 1, 3, 8}, 30] (* G. C. Greubel, Jan 11 2019 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x^2)/(1-3*x-x^3-x^4))) \\ G. C. Greubel, Jan 11 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-x^2)/(1-3*x-x^3-x^4) )); // G. C. Greubel, Jan 11 2019
(Sage) (x*(1-x^2)/(1-3*x-x^3-x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 11 2019
(GAP) a:=[0, 1, 3, 8];; for n in [5..30] do a[n]:=3*a[n-1]+a[n-3]+a[n-4]; od; a; # G. C. Greubel, Jan 11 2019

Crossrefs

Cf. A192232, A192744, A192904, A192872.

Sequence in context: A007563 A050383 A060404 * A192207 A289593 A101490

Adjacent sequences: A192902 A192903 A192904 * A192906 A192907 A192908

Keyword

nonn,easy

Author

Clark Kimberling, Jul 12 2011

Status

approved