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 A017897 #49 Nov 24 2024 10:45:59
%S A017897 1,17,202,2090,20251,189707,1745332,15900020,144066901,1301455397,
%T A017897 11737424062,105758621150,952437144751,8574983669087,77190104636392,
%U A017897 694787214149480,6253466332501801,56283104147438777,506557473488982322,4559064943373269010
%N A017897 Expansion of 1/((1-3*x)*(1-5*x)*(1-9*x)).
%H A017897 Vincenzo Librandi, <a href="/A017897/b017897.txt">Table of n, a(n) for n = 0..200</a>
%H A017897 Christian Brouder, William J. Keith, and Ângela Mestre, <a href="http://arxiv.org/abs/1301.0874">Closed forms for a multigraph enumeration</a>, arXiv preprint arXiv:1301.0874 [math.CO], 2013-2015.
%H A017897 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-87,135).
%F A017897 a(n) = term (1,1) in the 3 X 3 matrix [17,1,0; -87,0,1; 135,0,0]^n. - _Alois P. Heinz_, Aug 04 2008
%F A017897 From _Vincenzo Librandi_, Jul 01 2013: (Start)
%F A017897 a(n) = 17*a(n-1) - 87*a(n-2) + 135*a(n-3); a(0)=1, a(1)=17, a(2)=202.
%F A017897 a(n) = 14*a(n-1) - 45*a(n-2) + 3^n. (End)
%F A017897 a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24. - _Yahia Kahloune_, Aug 13 2013
%F A017897 E.g.f.: exp(3*x)*(6 - 25*exp(2*x) + 27*exp(6*x))/8. - _Stefano Spezia_, Nov 09 2024
%p A017897 a:= n -> (Matrix(3, (i,j)-> if (i=j-1) then 1 elif j=1 then [17, -87, 135][i] else 0 fi)^n)[1,1]: seq (a(n), n=0..25); # _Alois P. Heinz_, Aug 04 2008
%t A017897 CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t A017897 LinearRecurrence[{17,-87,135},{1,17,202},30] (* _Harvey P. Dale_, Sep 26 2014 *)
%t A017897 a[n_]:=(9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; Array[a, 30, 0] (* _Stefano Spezia_, Oct 04 2018 *)
%o A017897 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-9*x)))); // _Vincenzo Librandi_, Jul 01 2013
%o A017897 (Magma) I:=[1, 17, 202]; [n le 3 select I[n] else 17*Self(n-1)-87*Self(n-2)+135*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 01 2013
%o A017897 (PARI) a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; \\ _Joerg Arndt_, Aug 13 2013
%o A017897 (SageMath)
%o A017897 def A017897(n): return (9^(n+2) -3*5^(n+2) +2*3^(n+2))//24
%o A017897 [A017897(n) for n in range(41)] # _G. C. Greubel_, Nov 09 2024
%Y A017897 Cf. A005059, A016142, A016163.
%K A017897 nonn,easy
%O A017897 0,2
%A A017897 _N. J. A. Sloane_