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a(n) = 9^n - n^4.
2

%I #18 Aug 01 2022 15:30:07

%S 1,8,65,648,6305,58424,530145,4780568,43042625,387413928,3486774401,

%T 31381044968,282429515745,2541865799768,22876792416545,

%U 205891132044024,1853020188786305,16677181699583048,150094635296894145

%N a(n) = 9^n - n^4.

%H Vincenzo Librandi, <a href="/A024105/b024105.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (14,-55,100,-95,46,-9).

%F a(n) = 14*a(n-1) - 55*a(n-2) + 100*a(n-3) - 95*a(n-4) + 46*a(n-5) - 9*a(n-6); a(0)=1, a(1)=8, a(2)=65, a(3)=648, a(4)=6305, a(5)=58424. - _Harvey P. Dale_, Oct 07 2013

%F G.f.: (1 - 6*x + 8*x^2 + 78*x^3 + 103*x^4 + 8*x^5)/((1 - x)^5*(1 - 9*x)). - _Stefano Spezia_, Aug 01 2022

%t Table[9^n-n^4,{n,0,25}] (* or *) LinearRecurrence[{14,-55,100,-95,46,-9},{1,8,65,648,6305,58424},30] (* _Harvey P. Dale_, Oct 07 2013 *)

%o (Magma) [9^n-n^4: n in [0..25]]; // _Vincenzo Librandi_, Jul 06 2011

%Y Cf. A000583, A001019.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_