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%I #14 Jun 29 2023 23:59:50
%S 1,9,88,918,10012,112284,1280224,14735016,170493712,1978495632,
%T 22996386688,267526283616,3113740490176,36250383835584,
%U 422090112767488,4915093625981568,57237016922874112,666549376289097984
%N a(n) = ((9 + sqrt(7))^n + (9 - sqrt(7))^n)/2.
%C Binomial transform of A152265. - _Philippe Deléham_, Dec 03 2008
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -74).
%F From _Philippe Deléham_, Dec 03 2008: (Start)
%F a(n) = 18*a(n-1) - 74*a(n-2), n > 1; a(0)=1, a(1)=9.
%F G.f.: (1-9*x)/(1-18*x+74*x^2).
%F a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*7^(n-k). (End)
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((9+r7)^n+(9-r7)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 03 2008
%Y Cf. A098158, A152265.
%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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