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%I #21 Dec 25 2022 17:39:54
%S 1,8,71,680,6833,70568,739607,7811336,82823777,879934280,9357993191,
%T 99571637096,1059740581649,11280265991912,120079042716599,
%U 1278289521926600,13608126915979457,144867527905855112
%N a(n) = ((8 + sqrt(7))^n + (8 - sqrt(7))^n)/2.
%C Binomial transform of A145302. Inverse binomial transform of A152266. - _Philippe Deléham_, Dec 03 2008
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -57).
%F From _Philippe Deléham_, Dec 03 2008: (Start)
%F a(n) = 16*a(n-1) - 57*a(n-2), n > 1; a(0)=1, a(1)=8.
%F G.f.: (1-8*x)/(1-16*x+57*x^2).
%F a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*7^(n-k). (End)
%F a(n) = Sum_{k=1..n} A056241(n,k) * 7^(k-1). - _J. Conrad_, Nov 23 2022
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((8+r7)^n+(8-r7)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 03 2008
%Y Cf. A056241, A098158, A145302, A152266.
%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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