A063757 G.f.: (1+3*x+2*x^2)/((1-x)*(1-2*x^2)).

1, 4, 8, 14, 22, 34, 50, 74, 106, 154, 218, 314, 442, 634, 890, 1274, 1786, 2554, 3578, 5114, 7162, 10234, 14330, 20474, 28666, 40954, 57338, 81914, 114682, 163834, 229370, 327674, 458746, 655354, 917498, 1310714, 1835002, 2621434

Offset: 0

Author

N. J. A. Sloane, Aug 14 2001

Keywords

• nonn
• easy

References

• P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 158.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2).

Programs

Mathematica

CoefficientList[Series[(1+3x+2x^2)/((1-x)(1-2x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,-2},{1,4,8},41] (* Harvey P. Dale, Jun 05 2012 *)

Formula

a(0)=1, a(1)=4, a(2)=8, a(n)=a(n-1)+2*a(n-2)-2*a(n-3) From Harvey P. Dale, Jun 05 2012

a(n)=2^((n-3)/2)*((5*Sqrt[2]-7)*(-1)^n+7+5*Sqrt[2])-6 From Harvey P. Dale, Jun 05 2012

a(2*n) = 7*2^n - 6 = A048489(n), a(2*n+1) = 10*2^n - 6 = A020714(n+1) - 6, a(n) = A070875(n+1) - 6. - Philippe Deléham, Apr 13 2013