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 A152264 a(n) = ((9+sqrt(6))^n + (9-sqrt(6))^n)/2. 1

%I

%S 1,9,87,891,9513,104409,1165887,13155291,149353713,1701720009,

%T 19429431687,222100769691,2540606477913,29073358875609,

%U 332774973917487,3809447614844091,43611934023382113,499306241307571209

%N a(n) = ((9+sqrt(6))^n + (9-sqrt(6))^n)/2.

%C Binomial transform of A152263. - _Philippe Deléham_, Dec 03 2008

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -75).

%F From _Philippe Deléham_, Dec 03 2008: (Start)

%F a(n) = 18*a(n-1) - 75*a(n-2), n > 1; a(0)=1, a(1)=9.

%F G.f.: (1-9*x)/(1-18*x+75*x^2).

%F a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*6^(n-k). (End)

%o (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((9+r6)^n+(9-r6)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 03 2008

%K nonn

%O 0,2

%A Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

%E Extended beyond a(6) by _Klaus Brockhaus_, Dec 03 2008

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)