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A155599
a(n) = 8^n - 2^n + 1^n.
33
1, 7, 61, 505, 4081, 32737, 262081, 2097025, 16776961, 134217217, 1073740801, 8589932545, 68719472641, 549755805697, 4398046494721, 35184372056065, 281474976645121, 2251799813554177, 18014398509219841, 144115188075331585
OFFSET
0,2
FORMULA
G.f.: 1/(1-8*x) - 1/(1-2*x) + 1/(1-x).
E.g.f.: e^(8*x) - e^(2*x) + e^x.
a(n) = 10*a(n-1) - 16*a(n-2) + 7 with a(0)=1, a(1)=7 - Vincenzo Librandi, Jul 21 2010
a(n) = A248217(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[8^n-2^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{11, -26, 16}, {1, 7, 61}, 30] (* Harvey P. Dale, Feb 25 2014 *)
PROG
(PARI) a(n)=8^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved