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A154025
a(n+2) = 64*a(n+1) - a(n), a(1)=0, a(2)=8.
1
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.
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 04 2009
STATUS
approved