%I #7 Sep 08 2022 08:45:46
%S 2,9,44,226,1192,6372,34288,185096,1000736,5414544,29306048,158644768,
%T 858873472,4649961024,25175459584,136304222336,737977344512,
%U 3995559643392,21632794323968,117124519584256,634137036138496
%N a(n) = 8*a(n-1)-14*a(n-2) for n>1; a(0) = 2; a(1) = 9.
%C Fourth binomial transform of A135530.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-14).
%F G.f.: (2-7*x)/(1-8*x+14*x^2).
%F a(n) = ((4+sqrt(2))^(n+1)+(4-sqrt(2))^(n+1))/4.
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+r)^(n+1)+(4-r)^(n+1))/4: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ];
%Y Cf. A135530, A161944 (third binomial transform of A135530), A161947 (fifth binomial transform of A135530).
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, Jul 01 2009