A024145 - OEIS

%I #19 Sep 08 2022 08:44:48

%S 1,11,112,1485,19712,245707,2978208,35815001,429948928,5159721303,

%T 61917264224,743008209637,8916100199424,106993205007779,

%U 1283918464011040,15407021573826993,184884258893987840

%N a(n) = 12^n - n^5.

%H Vincenzo Librandi, <a href="/A024145/b024145.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (18,-87,200,-255,186,-73,12).

%F a(n) = 18*a(n-1) - 87*a(n-2) + 200*a(n-3) - 255*a(n-4) + 186*a(n-5) - 73*a(n-6) + 12*a(n-7); a(0)=1, a(1)=11, a(2)=112, a(3)=1485, a(4)=19712, a(5)=245707, a(6)=2978208. - _Harvey P. Dale_, Jul 19 2011

%F G.f.: (-13*x^6 - 305*x^5 - 781*x^4 - 226*x^3 - x^2 + 7*x - 1)/((x-1)^6*(12*x-1)). - _Harvey P. Dale_, Jul 19 2011

%t Table[12^n-n^5,{n,0,20}] (* or *) LinearRecurrence[ {18,-87,200,-255,186,-73,12},{1,11,112,1485,19712,245707,2978208},20] (* _Harvey P. Dale_, Jul 19 2011 *)

%o (Magma) [12^n-n^5: n in [0..20]]; // _Vincenzo Librandi_, Jul 01 2011

%o (PARI) a(n)=12^n-n^5 \\ _Charles R Greathouse IV_, Jul 01 2011

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_