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%I #29 Feb 19 2024 01:52:15
%S 1,19,326,5546,94287,1602885,27249052,463233892,7874976173,
%T 133874594951,2275868114178,38689757941038,657725884997659,
%U 11181340044960217,190082780764323704,3231407272993502984,54933923640889550745,933876701895122362683
%N a(1)=1, a(n)=17*a(n-1)+n.
%H Vincenzo Librandi, <a href="/A014900/b014900.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-35,17).
%F a(1)=1, a(2)=19, a(3)=326, a(n)=19*a(n-1)-35*a(n-2)+17*a(n-3). - _Vincenzo Librandi_, Oct 20 2012
%p a:=n->sum((17^(n-j)-1)/16,j=0..n): seq(a(n), n=1..16); # _Zerinvary Lajos_, Jan 05 2007
%p a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,17]])^n)[2,3]:
%p seq(a(n), n=1..16); # _Alois P. Heinz_, Aug 06 2008
%t LinearRecurrence[{19, -35, 17}, {1, 19, 326}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%t nxt[{n_,a_}]:={n+1,17a+n+1}; NestList[nxt,{1,1},20][[All,2]] (* _Harvey P. Dale_, Jun 19 2021 *)
%o (Magma) I:=[1, 19, 326]; [n le 3 select I[n] else 19*Self(n-1) - 35*Self(n-2) + 17*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Olivier Gérard_
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