%I #12 Sep 08 2022 08:45:47
%S 1,17,153,1241,9809,76993,603177,4722889,36974881,289459697,
%T 2266023993,17739425081,138871842929,1087148202913,8510660699337,
%U 66625087543849,521569643549761,4083069947252177,31964015532175833,250227966218471321
%N a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
%C Binomial transform of A164542. Fifth binomial transform of A164675.
%H Vincenzo Librandi, <a href="/A164543/b164543.txt">Table of n, a(n) for n = 0..144</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -17).
%F a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
%F G.f.: (1+7*x)/(1-10*x+17*x^2).
%F a(n) = ((1+3*sqrt(2))*(5+2*sqrt(2))^n + (1-3*sqrt(2))*(5-2*sqrt(2))^n)/2.
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(5+2*r)^n+(1-3*r)*(5-2*r)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 20 2009
%Y Cf. A164542, A164675.
%K nonn,easy
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 20 2009
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