A154025 a(n+2) = 64*a(n+1) - a(n), a(1)=0, a(2)=8.

0, 8, 512, 32760, 2096128, 134119432, 8581547520, 549084921848, 35132853450752, 2247953535926280, 143833893445831168, 9203121226997268472, 588855924634379351040, 37677576055373281198088, 2410776011619255617326592

Offset

1,2

Comments

If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=64.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

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

Formula

G.f.: 8*x^2/(1 -64*x +x^2). - R. J. Mathar, Jan 05 2011

Mathematica

CoefficientList[Series[(8z)/(z^2-64z+1), {z, 0, 20}], z] (* Vincenzo Librandi, Jan 29 2012 *)
LinearRecurrence[{64, -1}, {0, 8}, 20] (* Harvey P. Dale, Dec 19 2023 *)

Prog

(Magma) I:=[0, 8]; [n le 2 select I[n] else 64*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jan 29 2012
(PARI) a(n)=([0, 1; -1, 64]^(n-1)*[0; 8])[1, 1] \\ Charles R Greathouse IV, Sep 01 2016

Crossrefs

Cf. A065100, A154021-A154027.

Sequence in context: A128794 A195804 A145259 * A013713 A109966 A139567

Adjacent sequences: A154022 A154023 A154024 * A154026 A154027 A154028

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 04 2009

Status

approved