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%I #13 Sep 08 2022 08:45:47
%S 5,28,154,840,4564,24752,134120,726432,3933776,21300160,115328416,
%T 624425088,3380802880,18304471808,99104534144,536573667840,
%U 2905125864704,15728975567872,85160042437120,461074681546752
%N a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 28.
%C Binomial transform of A102285 without initial term 1. Fourth binomial transform of A164682. Inverse binomial transform of A164538.
%H Vincenzo Librandi, <a href="/A164537/b164537.txt">Table of n, a(n) for n = 0..158</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -14).
%F a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 28.
%F G.f.: (5-12*x)/(1-8*x+14*x^2).
%F a(n) = ((5+4*sqrt(2))*(4+sqrt(2))^n + (5-4*sqrt(2))*(4-sqrt(2))^n)/2.
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+4*r)*(4+r)^n+(5-4*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 21 2009
%Y Cf. A102285, A164682, A164538.
%K nonn,easy
%O 0,1
%A Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 21 2009