OFFSET
0,3
COMMENTS
Binomial transform of A001026 (powers of 17), with interpolated zeros .
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,16).
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
MATHEMATICA
LinearRecurrence[{2, 16}, {1, 1}, 30] (* Harvey P. Dale, Dec 12 2012 *)
PROG
(PARI) Vec((1-x)/(1-2*x-16*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
(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
(SageMath)
A133356=BinaryRecurrenceSequence(2, 16, 1, 1)
[A133356(n) for n in range(41)] # G. C. Greubel, Oct 15 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Dec 21 2007
STATUS
approved