|
%I #14 Sep 03 2019 03:37:04
%S 1,2,9,30,109,386,1377,4902,17461,62186,221481,788814,2809405,
%T 10005842,35636337,126920694,452034757,1609945658,5733906489,
%U 20421610782,72732645325,259041157538,922588763265,3285848604870,11702723341141
%N a(n) = 2*a(n-1) + 5*a(n-2) + 2*a(n-3).
%C Transform of 2^n under Riordan array A101603.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,5,2).
%F G.f.: 1/((1+x)*(1-3*x-2*x^2));
%F a(n) = (3/4 + sqrt(17)/4)^n*(1/4 + 7*sqrt(17)/68) + (1/4 - 7*sqrt(17)/68)*(3/4 - sqrt(17)/4)^n + (-1)^n/2;
%F a(n) = (A007483(n) + (-1)^n)/2. - _R. J. Mathar_, Sep 21 2012
%Y Cf. A007483, A101603.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 08 2004
|
