A174192 Expansion of (1-x+2x^2)/ ((1-x)*(1-2x-x^2)).

1, 2, 7, 18, 45, 110, 267, 646, 1561, 3770, 9103, 21978, 53061, 128102, 309267, 746638, 1802545, 4351730, 10506007, 25363746, 61233501, 147830750, 356895003, 861620758, 2080136521, 5021893802, 12123924127

Offset: 0

Author

Clark Kimberling, Mar 11 2010

Keywords

• nonn

Examples

			a(2) = 2*a(1)+a(0)+2 = 2*2+1+2 = 7
a(3) = 2*a(2)+a(1)+2 = 2*7+2+2 = 18.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-1)

Crossrefs

Cf. A174191, A048655 (first differences)

Programs

Mathematica

CoefficientList[Series[(1-x+2x^2)/((1-x)*(1-2x-x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{3,-1,-1},{1,2,7},30] (* Harvey P. Dale, Jul 18 2019 *)

Formula

a(n)=2*a(n-1)+a(n-2)+2, with a(0)=1, a(1)=2.

Extensions

Terms corrected by R. J. Mathar, Oct 26 2011