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%I #30 Jan 01 2024 11:44:34
%S 1,1,18,52,392,1616,9504,44864,241792,1201408,6271488,31765504,
%T 163874816,835997696,4293992448,21963948032,112631775232,576686718976,
%U 2955481841664,15137951186944,77563611840512,397334442672128
%N a(n) = 2*a(n-1) + 16*a(n-2) for n>1, a(0)=1, a(1)=1.
%C Binomial transform of A001026 (powers of 17), with interpolated zeros .
%H Harvey P. Dale, <a href="/A133356/b133356.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,16).
%F G.f.: (1-x)/(1-2*x-16*x^2).
%F a(n) = Sum_{k=0..n} A098158(n,k)*17^(n-k). - _Philippe Deléham_, Dec 26 2007
%F If p[1]=1, and p[i]=17, (i>1), and if A is Hessenberg matrix of order n defined by: A[i,j] = p[j-i+1], (i<=j), A[i,j] = -1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det A. - _Milan Janjic_, Apr 29 2010
%F a(n) = (4*i)^(n-1)*(4*i*ChebyshevU(n, -i/4) - ChebyshevU(n-1, -i/4)) = A161007(n) - A161007(n-1). - _G. C. Greubel_, Oct 15 2022
%t LinearRecurrence[{2,16},{1,1},30] (* _Harvey P. Dale_, Dec 12 2012 *)
%o (PARI) Vec((1-x)/(1-2*x-16*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 12 2012
%o (Magma) [n le 2 select 1 else 2*(Self(n-1) +8*Self(n-2)): n in [1..41]]; // _G. C. Greubel_, Oct 15 2022
%o (SageMath)
%o A133356=BinaryRecurrenceSequence(2,16,1,1)
%o [A133356(n) for n in range(41)] # _G. C. Greubel_, Oct 15 2022
%Y First differences of A161007.
%Y Cf. A001026, A098158, A161007.
%K nonn,easy
%O 0,3
%A _Philippe Deléham_, Dec 21 2007
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