A158798 a(n) = a(n-1) + 64*a(n-2), a(0)=1, a(1)=8.

1, 8, 72, 584, 5192, 42568, 374856, 3099208, 27089992, 225439304, 1959198792, 16387314248, 141776036936, 1190564148808, 10264230512712, 86460336036424, 743371088849992, 6276832595181128, 53852582281580616, 455569868373172808, 3902135134394332232

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,64).

Formula

G.f.: (1+7*x)/(1-x-64*x^2).

a(n) = (8*i)^n*( ChebyshevU(n, -i/16) - (7*i/8)*ChebyshevU(n-1, -i/16) ). - G. C. Greubel, Dec 22 2021

Mathematica

LinearRecurrence[{1, 64}, {1, 8}, 30] (* Harvey P. Dale, Mar 09 2018 *)

Prog

(Magma) I:=[1, 8]; [n le 2 select I[n] else Self(n-1) + 64*Self(n-2): n in [1..41]]; // G. C. Greubel, Dec 22 2021
(SageMath) [(8*i)^n*( chebyshev_U(n, -i/16) - (7*i/8)*chebyshev_U(n-1, -i/16) ) for n in (0..40)] # G. C. Greubel, Dec 22 2021
(PARI) a(n)=([0, 1; 64, 1]^n*[1; 8])[1, 1] \\ Charles R Greathouse IV, May 27 2026

Crossrefs

Cf. A000045, A026597, A122994, A122995, A122996, A158608, A158797.

Sequence in context: A111919 A052379 A246940 * A229249 A242160 A343365

Adjacent sequences: A158795 A158796 A158797 * A158799 A158800 A158801

Keyword

nonn,easy,changed

Author

Philippe Deléham, Mar 27 2009

Extensions

Corrected and extended by Harvey P. Dale, Mar 09 2018

Status

approved