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 A016201 #24 Mar 29 2025 16:54:17
%S A016201 1,10,77,554,3909,27426,192109,1345018,9415637,65910482,461375421,
%T A016201 3229632042,22607432485,158252043778,1107764339213,7754350440026,
%U A016201 54280453211253,379963172740914,2659742209710685,18618195469023370,130327368285260741,912291578001019490,6386041046015525037
%N A016201 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-7*x)).
%H A016201 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23,14).
%F A016201 a(n) = (49*7^n - 24*2^n + 5)/30. - _Bruno Berselli_, Feb 09 2011
%F A016201 a(0)=1, a(n) = 7*a(n-1) + 2^(n+1) - 1. - _Vincenzo Librandi_, Feb 09 2011
%F A016201 From _Elmo R. Oliveira_, Mar 27 2025: (Start)
%F A016201 E.g.f.: exp(x)*(49*exp(6*x) - 24*exp(x) + 5)/30.
%F A016201 a(n) = 10*a(n-1) - 23*a(n-2) + 14*a(n-3).
%F A016201 a(n) = A016130(n+1) - A023000(n+2). (End)
%p A016201 a:=n->sum((7^(n-j+1)-2^(n-j+1))/5, j=0..n+1): seq(a(n), n=0..19); # _Zerinvary Lajos_, Jan 15 2007
%t A016201 CoefficientList[Series[1/((1-x)(1-2x)(1-7x)),{x,0,20}],x](* or *) LinearRecurrence[{10,-23,14},{1,10,77},20] (* _Harvey P. Dale_, Mar 06 2019 *)
%Y A016201 Cf. A016130, A023000.
%K A016201 nonn,easy
%O A016201 0,2
%A A016201 _N. J. A. Sloane_
%E A016201 More terms from _Elmo R. Oliveira_, Mar 27 2025