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%I #20 Dec 26 2023 13:08:19
%S 1,8,67,584,5257,48488,455131,4324328,41426257,399036104,3857575987,
%T 37380013448,362768079961,3524108459048,34256882467147,
%U 333139503472424,3240562225062817,31527485889187208,306765478498163491
%N a(n) = ((8 + sqrt(3))^n + (8 - sqrt(3))^n)/2.
%H Harvey P. Dale, <a href="/A152055/b152055.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -61).
%F From _Philippe Deléham_, Nov 26 2008: (Start)
%F a(n) = 16*a(n-1) - 61*a(n-2), n > 1; a(0)=1, a(1)=8.
%F G.f.: (1-8*x)/(1-16x+61*x^2).
%F a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2*k)*3^(n-k))/8^n. (End)
%t LinearRecurrence[{16,-61},{1,8},30] (* _Harvey P. Dale_, Sep 02 2018 *)
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((8+r3)^n+(8-r3)^n)/2: n in [0..18] ]; [ 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_ and _Philippe Deléham_, Nov 26 2008
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