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%I #15 Sep 08 2022 08:45:47
%S 1,21,193,1573,12449,97749,765857,5996837,46948801,367541781,
%T 2877288193,22524671653,176332817249,1380408754389,10806429650657,
%U 84597347681957,662264172758401,5184486816990741,40586377233014593,317727496441303333
%N a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 21.
%C Binomial transform of A164605. Fifth binomial transform of A164702.
%H G. C. Greubel, <a href="/A164606/b164606.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..144 from Vincenzo Librandi)
%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) = 21.
%F a(n) = ((1+4*sqrt(2))*(5+2*sqrt(2))^n + (1-4*sqrt(2))*(5-2*sqrt(2))^n)/2.
%F G.f.: (1+11*x)/(1-10*x+17*x^2).
%F E.g.f.: exp(5*x)*(cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x)). - _G. C. Greubel_, Aug 10 2017
%t LinearRecurrence[{10,-17},{1,21},30] (* _Harvey P. Dale_, May 22 2013 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(5+2*r)^n+(1-4*r)*(5-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 23 2009
%o (PARI) x='x+O('x^50); Vec((1+11*x)/(1-10*x+17*x^2)) \\ _G. C. Greubel_, Aug 10 2017
%Y Cf. A164605, A164702.
%K nonn,easy
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 23 2009