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A014899 a(n) = (16^(n+1) - 15*n - 16)/225.

%I A014899 #40 Mar 31 2025 17:19:36
%S A014899 0,1,18,291,4660,74565,1193046,19088743,305419896,4886718345,
%T A014899 78187493530,1250999896491,20015998343868,320255973501901,
%U A014899 5124095576030430,81985529216486895,1311768467463790336,20988295479420645393,335812727670730326306,5373003642731685220915
%N A014899 a(n) = (16^(n+1) - 15*n - 16)/225.
%H A014899 Vincenzo Librandi, <a href="/A014899/b014899.txt">Table of n, a(n) for n = 0..200</a>
%H A014899 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-33,16).
%F A014899 a(n) = 16*a(n-1) + n = 18*a(n-1) - 33*a(n-2) + 16*a(n-3).
%F A014899 G.f.: x/((1-16*x)*(x-1)^2). - _R. J. Mathar_, Apr 29 2010
%F A014899 E.g.f.: exp(x)*(16*exp(15*x) - 15*x - 16)/225. - _Elmo R. Oliveira_, Mar 31 2025
%p A014899 a:=n->sum((16^(n-j)-1)/15,j=0..n): seq(a(n), n=1..16); # _Zerinvary Lajos_, Jan 05 2007
%p A014899 n0:=20: tabl:=array(1..n0-1): for n from 0 to n0 do: tabl[n+1]:=(4^(2*n+2) - 15*n - 16)/225:od:print( tabl): # _Michel Lagneau_, Apr 26 2010
%t A014899 s=0;lst={};Do[AppendTo[lst,s+=s+=s+=s+=s+=n],{n,5!}];lst/16 (* _Vladimir Joseph Stephan Orlovsky_, Oct 20 2009 *)
%t A014899 Table[(16^(n+1)-15*n-16)/225,{n,0,20}] (* _Harvey P. Dale_, Dec 20 2010 *)
%t A014899 LinearRecurrence[{18, -33, 16}, {0, 1, 18}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%o A014899 (Magma) I:=[0, 1, 18]; [n le 3 select I[n] else 18*Self(n-1) - 33*Self(n-2) + 16*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012
%o A014899 (Maxima) A014899(n):=(16^(n+1)-15*n-16)/225$ makelist(A014899(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%o A014899 (PARI) a(n)=(16^(n+1)-15*n)\225 \\ _Charles R Greathouse IV_, May 15 2013
%Y A014899 Row n=16 of A126885.
%K A014899 nonn,easy
%O A014899 0,3
%A A014899 _N. J. A. Sloane_, _Olivier Gérard_
%E A014899 a(0) added by _R. J. Mathar_, Apr 29 2010