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%I #29 May 10 2020 13:44:38
%S 3,13,91,757,6643,59293,532171,4785157,43053283,387440173,3486843451,
%T 31381236757,282430067923,2541867422653,22876797237931,
%U 205891146443557,1853020231898563,16677181828806733,150094635684419611
%N a(n) = 1^n + 3^n + 9^n.
%C Also the sum of n-th powers of the divisors of 9.
%H T. D. Noe, <a href="/A034513/b034513.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).
%F G.f.: 1/(1-x)+1/(1-3*x)+1/(1-9*x). E.g.f.: e^x+e^(3*x)+e^(9*x). - _Mohammad K. Azarian_, Dec 26 2008
%F a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3), a(0)=3, a(1)=13, a(2)=91. - _Harvey P. Dale_, Apr 13 2012
%t Table[1^n + 3^n + 9^n, {n, 0, 20}]
%t LinearRecurrence[{13,-39,27},{3,13,91},20] (* _Harvey P. Dale_, Apr 13 2012 *)
%o (Sage) [sigma(9,n)for n in range(0,19)] # _Zerinvary Lajos_, Jun 04 2009
%o (PARI) a(n)=1+3^n+9^n \\ _Charles R Greathouse IV_, Jun 10 2011
%Y Cf. A001550, A001576, A001579, A074501-A074580.
%K easy,nonn
%O 0,1
%A _N. J. A. Sloane_
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