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%I #17 Sep 08 2022 08:45:47
%S 1,10,72,496,3392,23168,158208,1080320,7376896,50372608,343965696,
%T 2348744704,16038232064,109515898880,747821334528,5106443485184,
%U 34868977205248,238100269760512,1625850340442112,11102000565452800
%N a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
%C Binomial transform of A038761. Fourth binomial transform of A164640. Inverse binomial transform of A164547.
%H Vincenzo Librandi, <a href="/A164546/b164546.txt">Table of n, a(n) for n = 0..149</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8).
%F a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
%F a(n) = ((2+3*sqrt(2))*(4+2*sqrt(2))^n + (2-3*sqrt(2))*(4-2*sqrt(2))^n)/4.
%F G.f.: (1 + 2*x)/(1 - 8*x + 8*x^2).
%F a(n) = 2*(2*sqrt(2))^(n-1)*(sqrt(2)*chebyshev_U(n, sqrt(2)) + chebyshev_U(n-1, sqrt(2))). - _G. C. Greubel_, Jul 17 2021
%t LinearRecurrence[{8,-8}, {1,10}, 30] (* _G. C. Greubel_, Jul 17 2021 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(4+2*r)^n+(2-3*r)*(4-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 19 2009
%o (Sage) [2*(2*sqrt(2))^(n-1)*(sqrt(2)*chebyshev_U(n, sqrt(2)) + chebyshev_U(n-1, sqrt(2))) for n in (0..30)] # _G. C. Greubel_, Jul 17 2021
%Y Cf. A038761, A164640, A164547.
%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 19 2009
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