OFFSET
0,1
COMMENTS
a(n) is nonnegative since the real root of x^3-2*x^2+2*x-2 is dominant. - Michael Somos, Feb 28 2007
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..5303
Yassine Otmani, The 2-Pascal Triangle and a Related Riordan Array, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 21.
N. J. A. Sloane, Transforms
Index entries for linear recurrences with constant coefficients, signature (2,-2,2).
FORMULA
a(n)=2a(n-1)-2a(n-2)+2a(n-3), a(0)=3, a(1)=2, a(2)=0.
G.f.: (3 - 4*x + 2*x^2)/(1 - 2*x + 2*x^2 - 2*x^3).
MATHEMATICA
CoefficientList[Series[(3-4*x+2*x^2)/(1-2*x+2*x^2-2*x^3), {x, 0, 40}], x]
LinearRecurrence[{2, -2, 2}, {3, 2, 0}, 40] (* Harvey P. Dale, Jan 24 2019 *)
PROG
(PARI) {a(n)= if(n<0, 0, polsym( x^3 -2*x^2 +2*x -2, n) [n+1])} /* Michael Somos, Feb 28 2007 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Sep 02 2002
STATUS
approved