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 A016145 #35 Mar 16 2025 17:25:52
%S A016145 1,13,139,1417,14251,142753,1428259,14284777,142854331,1428562993,
%T A016145 14285688979,142857066937,1428571200811,14285713602433,
%U A016145 142857140807299,1428571422421897,14285714267265691,142857142801797073,1428571428405391219,14285714285216173657,142857142855648520971
%N A016145 Expansion of g.f. 1/((1-3*x)*(1-10*x)).
%H A016145 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-30).
%F A016145 a(n) = (10^(n+1) - 3^(n+1))/7 = 10*a(n-1) + 3^n = 3*a(n-1) + 10^n. - _Henry Bottomley_, Jul 25 2001
%F A016145 a(n) = 13*a(n-1) - 30*a(n-2), n >= 2. - _Vincenzo Librandi_, Mar 14 2011
%F A016145 From _Elmo R. Oliveira_, Mar 08 2025: (Start)
%F A016145 E.g.f.: exp(3*x)*(10*exp(7*x) - 3)/7.
%F A016145 a(n) = A248226(n+1)/7. (End)
%t A016145 Join[{a=1,b=13},Table[c=13*b-30*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t A016145 CoefficientList[Series[1/((1-3x)(1-10x)),{x,0,20}],x] (* or *) LinearRecurrence[{13,-30},{1,13},20] (* _Harvey P. Dale_, May 04 2018 *)
%Y A016145 Cf. A248226.
%K A016145 nonn,easy
%O A016145 0,2
%A A016145 _N. J. A. Sloane_