A133356 a(n) = 2*a(n-1) + 16*a(n-2) for n>1, a(0)=1, a(1)=1.
1, 1, 18, 52, 392, 1616, 9504, 44864, 241792, 1201408, 6271488, 31765504, 163874816, 835997696, 4293992448, 21963948032, 112631775232, 576686718976, 2955481841664, 15137951186944, 77563611840512, 397334442672128
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,16).
Programs
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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
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Mathematica
LinearRecurrence[{2,16},{1,1},30] (* Harvey P. Dale, Dec 12 2012 *) -
PARI
Vec((1-x)/(1-2*x-16*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
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SageMath
A133356=BinaryRecurrenceSequence(2,16,1,1) [A133356(n) for n in range(41)] # G. C. Greubel, Oct 15 2022
Formula
G.f.: (1-x)/(1-2*x-16*x^2).
a(n) = Sum_{k=0..n} A098158(n,k)*17^(n-k). - Philippe Deléham, Dec 26 2007
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
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
Comments