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%I #16 Jun 13 2015 00:50:29
%S 1,4,8,14,22,34,50,74,106,154,218,314,442,634,890,1274,1786,2554,3578,
%T 5114,7162,10234,14330,20474,28666,40954,57338,81914,114682,163834,
%U 229370,327674,458746,655354,917498,1310714,1835002,2621434
%N G.f.: (1+3*x+2*x^2)/((1-x)*(1-2*x^2)).
%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 158.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2).
%F 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
%F a(n)=2^((n-3)/2)*((5*Sqrt[2]-7)*(-1)^n+7+5*Sqrt[2])-6 From _Harvey P. Dale_, Jun 05 2012
%F 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
%t 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 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Aug 14 2001
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