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%I #15 Sep 08 2022 08:45:38
%S 1,8,72,704,7232,76288,815616,8777728,94769152,1024753664,11088986112,
%T 120037572608,1299617939456,14071782965248,152369922834432,
%U 1649898919297024,17865667030024192,193456332999753728
%N a(n) = ((8 + sqrt(8))^n + (8 - sqrt(8))^n)/2.
%C Binomial transform is A152267, inverse binomial transform is A147689.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -56).
%F From _R. J. Mathar_, Oct 10 2008: (Start)
%F a(n) = 16*a(n-1) - 56*a(n-2).
%F G.f.: (1-8x)/(1-16x+56x^2).
%F a(n) = 2^n*A081180(n+1) - 2^(n+2)*A081180(n). (End)
%F a(n) = Sum_{k=0..n} 8^k*A098158(n,k). - _Philippe Deléham_, Oct 14 2008
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((8+r8)^n+(8-r8)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Oct 20 2008
%Y Cf. A081180, A098158, A152267, A147689.
%K nonn
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008
%E More terms from _R. J. Mathar_, Oct 10 2008
%E Edited by _Klaus Brockhaus_, Jul 09 2009
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