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

Author

Vincenzo Librandi, Jan 04 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A065100, A154021-A154027.

Programs

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

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 *)

PARI

a(n)=([0,1; -1,64]^(n-1)*[0;8])[1,1] \\ Charles R Greathouse IV, Sep 01 2016

Formula

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