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A152263 a(n) = ((8 + sqrt(6))^n + (8 - sqrt(6))^n)/2.

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%I A152263 #13 Jun 29 2023 23:58:37
%S A152263 1,8,70,656,6436,64928,665560,6883136,71527696,745221248,7774933600,
%T A152263 81176105216,847871534656,8857730451968,92547138221440,
%U A152263 967005845328896,10104359508418816,105583413105625088,1103281758201710080
%N A152263 a(n) = ((8 + sqrt(6))^n + (8 - sqrt(6))^n)/2.
%C A152263 Binomial transform of A152262. Inverse binomial transform of A152264. - _Philippe Deléham_, Dec 03 2008
%H A152263 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -58).
%F A152263 From _Philippe Deléham_, Dec 03 2008: (Start)
%F A152263 a(n) = 16*a(n-1) - 58*a(n-2), n > 1; a(0)=1, a(1)=8.
%F A152263 G.f.: (1-8*x)/(1-16*x+58*x^2).
%F A152263 a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*6^(n-k). (End)
%t A152263 LinearRecurrence[{16,-58},{1,8},20] (* _Harvey P. Dale_, Jul 09 2021 *)
%o A152263 (Magma) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((8+r6)^n+(8-r6)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 03 2008
%K A152263 nonn
%O A152263 0,2
%A A152263 Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008
%E A152263 Extended beyond a(6) by _Klaus Brockhaus_, Dec 03 2008