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A163448 a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.

%I A163448 #19 Sep 08 2022 08:45:46
%S A163448 1,12,142,1664,19364,224208,2586488,29757376,341671696,3917211072,
%T A163448 44860395232,513321219584,5870105658944,67096633659648,
%U A163448 766662318616448,8757776273683456,100022618249257216,1142190290164165632
%N A163448 a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
%C A163448 Binomial transform of A163447. Tenth binomial transform of A163403.
%H A163448 G. C. Greubel, <a href="/A163448/b163448.txt">Table of n, a(n) for n = 0..940</a> (first 100 terms from Vincenzo Librandi)
%H A163448 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -98).
%F A163448 a(n) = ((1+sqrt(2))*(10+sqrt(2))^n + (1-sqrt(2))*(10-sqrt(2))^n)/2.
%F A163448 G.f.: (1-8*x)/(1-20*x+98*x^2).
%F A163448 a(n) = (31*(10-sqrt(2))^n - 41*sqrt(2)*(10-sqrt(2))^n + 49*(10+sqrt(2))^n + 49*sqrt(2)*(10+sqrt(2))^n)/(98*(10+sqrt(2))). - _Harvey P. Dale_, Nov 14 2011
%F A163448 E.g.f.: exp(10*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 24 2016
%t A163448 LinearRecurrence[{20,-98},{1,12},30] (* or *) With[{ms=10-Sqrt[2], ps=10+ Sqrt[2]},Table[Simplify[(31ms^n-41Sqrt[2](ms^n)+49ps^n+49Sqrt[2] ps^n)/ (98ps)],{n,20}]] (* _Harvey P. Dale_, Nov 14 2011 *)
%o A163448 (Magma) [ n le 2 select 11*n-10 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];
%o A163448 (PARI) Vec((1-8*x)/(1-20*x+98*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 24 2016
%Y A163448 Cf. A163403, A163447.
%K A163448 nonn
%O A163448 0,2
%A A163448 _Klaus Brockhaus_, Jul 27 2009