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A155623
a(n) = 11^n + 3^n - 1.
13
1, 13, 129, 1357, 14721, 161293, 1772289, 19489357, 214365441, 2357967373, 25937483649, 285311847757, 3138428908161, 34522713738253, 379749838366209, 4177248183764557, 45949729906618881, 505447028628433933
OFFSET
0,2
COMMENTS
a^n+b^n-1^n=(a+b)*a(n-1)-(a*b)*a(n-2)-(a-1)*(b-1) - Vincenzo Librandi, Jul 21 2010
FORMULA
G.f.: 1/(1 - 11*x) + 1/(1 - 3*x) - 1/(1 - x).
E.g.f.: exp(11*x) + exp(3*x) - exp(x).
a(n) = 14*a(n-1) - 33*a(n-2) - 20 for n>1, a(0)=1, a(1)=13 - Vincenzo Librandi, Jul 21 2010
MATHEMATICA
LinearRecurrence[{15, -47, 33}, {1, 13, 129}, 20] (* Harvey P. Dale, Jan 14 2015 *)
PROG
(PARI) a(n)=11^n+3^n-1 \\ Charles R Greathouse IV, Jun 11 2015
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 29 2009
STATUS
approved