A152056 - OEIS

%I #13 Jun 29 2023 23:55:10

%S 1,9,84,810,8028,81324,837648,8734392,91882512,972602640,10340011584,

%T 110257202592,1178108743104,12605895573696,135013638364416,

%U 1446985635811200,15514677652177152,166399318145915136

%N a(n) = ((9+sqrt(3))^n + (9-sqrt(3))^n)/2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -78).

%F From _Philippe Deléham_, Nov 26 2008: (Start)

%F a(n) = 18*a(n-1) - 78*a(n-2), n > 1; a(0)=1, a(1)=9.

%F G.f.: (1-9*x)/(1-18*x+78*x^2).

%F a(n) = (Sum_{k=0..n} A098158(n,k)*3^(3*k))/3^n. (End)

%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((9+r3)^n+(9-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Nov 26 2008

%K nonn

%O 0,2

%A Al Hakanson (hawkuu(AT)gmail.com), Nov 22 2008

%E Extended beyond a(6) by _Klaus Brockhaus_, Nov 26 2008