This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014901 #38 Mar 31 2025 15:37:54
%S A014901 1,20,363,6538,117689,2118408,38131351,686364326,12354557877,
%T A014901 222382041796,4002876752339,72051781542114,1296932067758065,
%U A014901 23344777219645184,420205989953613327,7563707819165039902,136146740744970718253,2450641333409472928572,44111544001370512714315
%N A014901 a(1)=1, a(n) = 18*a(n-1) + n.
%H A014901 Vincenzo Librandi, <a href="/A014901/b014901.txt">Table of n, a(n) for n = 1..200</a>
%H A014901 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-37,18).
%F A014901 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
%F A014901 From _Elmo R. Oliveira_, Mar 29 2025: (Start)
%F A014901 G.f.: x/((1-18*x)*(1-x)^2).
%F A014901 E.g.f.: exp(x)*(18*exp(17*x) - 17*x - 18)/289.
%F A014901 a(n) = (18^(n+1) - 17*n - 18)/289. (End)
%F A014901 a(-1-n) = A014935(n)/18^n for all n in Z. - _Michael Somos_, Mar 29 2025
%t A014901 LinearRecurrence[{20, -37, 18}, {1, 20, 363}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%t A014901 nxt[{n_,a_}]:={n+1,18a+n+1}; NestList[nxt,{1,1},20][[All,2]] (* _Harvey P. Dale_, Oct 08 2017 *)
%o A014901 (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 A014901 (Maxima)
%o A014901 a[1]:1$
%o A014901 a[2]:20$
%o A014901 a[3]:363$
%o A014901 a[n]:=20*a[n-1]-37*a[n-2]+18*a[n-3]$
%o A014901 A014901(n):=a[n]$
%o A014901 makelist(A014901(n),n,1,30); /* _Martin Ettl_, Nov 06 2012 */
%Y A014901 Row n=18 of A126885.
%Y A014901 Cf. A014935.
%K A014901 nonn,easy
%O A014901 1,2
%A A014901 _N. J. A. Sloane_, _Olivier Gérard_