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%I #31 Feb 19 2024 01:52:32
%S 1,20,363,6538,117689,2118408,38131351,686364326,12354557877,
%T 222382041796,4002876752339,72051781542114,1296932067758065,
%U 23344777219645184,420205989953613327,7563707819165039902,136146740744970718253
%N a(1)=1, a(n) = 18*a(n-1) + n.
%H Vincenzo Librandi, <a href="/A014901/b014901.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 (20, -37, 18).
%F a(1)=1, a(2)=20, a(3)=363, a(n) = 20*a(n-1) - 37*a(n-2) + 18*a(n-3). - _Vincenzo Librandi_, Oct 20 2012
%t LinearRecurrence[{20, -37, 18}, {1, 20, 363}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%t nxt[{n_,a_}]:={n+1,18a+n+1}; NestList[nxt,{1,1},20][[All,2]] (* _Harvey P. Dale_, Oct 08 2017 *)
%o (Magma) I:=[1, 20, 363]; [n le 3 select I[n] else 20*Self(n-1) - 37*Self(n-2) + 18*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012
%o (Maxima)
%o a[1]:1$
%o a[2]:20$
%o a[3]:363$
%o a[n]:=20*a[n-1]-37*a[n-2]+18*a[n-3]$
%o A014901(n):=a[n]$
%o makelist(A014901(n),n,1,30); /* _Martin Ettl_, Nov 06 2012 */
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Olivier Gérard_
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