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 + 1.
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)/( 1-3*x-x^3-x^4 ). - R. J. Mathar, Jul 13 2011
MATHEMATICA
(See A192906.)
LinearRecurrence[{3, 0, 1, 1}, {0, 1, 4, 12}, 30] (* G. C. Greubel, Jan 11 2019 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+x)/(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)/(1-3*x-x^3-x^4) )); // G. C. Greubel, Jan 11 2019
(Sage) (x*(1+x)/(1-3*x-x^3-x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 11 2019
(GAP) a:=[0, 1, 4, 12];; 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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 12 2011
STATUS
approved