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 A016313 #29 Dec 24 2024 22:12:09
%S A016313 1,19,257,3047,33825,361767,3782353,38976439,397835009,4034844935,
%T A016313 40743914289,410207399511,4121451795553,41350162566823,
%U A016313 414451137963665,4151157965737463,41558105760145857,415906740320988231
%N A016313 Expansion of 1/((1-2*x)*(1-7*x)*(1-10*x)).
%H A016313 Vincenzo Librandi, <a href="/A016313/b016313.txt">Table of n, a(n) for n = 0..200</a>
%H A016313 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-104,140).
%F A016313 a(0)=1, a(1)=19, a(2)=257, a(n)=19*a(n-1)-104*a(n-2)+140*a(n-3). - _Harvey P. Dale_, May 02 2012
%F A016313 a(n) = 2^n/10 - 49*7^n/15 + 25*10^n/6. - _R. J. Mathar_, Jun 23 2013
%F A016313 a(n) = 17*a(n-1) - 70*a(n-2) + 2^n. - _Vincenzo Librandi_, Jun 26 2013
%t A016313 CoefficientList[Series[1/((1-2x)(1-7x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{19,-104,140},{1,19,257},30] (* _Harvey P. Dale_, May 02 2012 *)
%o A016313 (PARI) Vec(1/((1-2*x)*(1-7*x)*(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A016313 (Magma) I:=[1, 19, 257]; [n le 3 select I[n] else 19*Self(n-1)-104*Self(n-2) +140*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jun 26 2013
%o A016313 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-7*x)*(1-10*x)))); // _Vincenzo Librandi_, Jun 26 2013
%K A016313 nonn,easy
%O A016313 0,2
%A A016313 _N. J. A. Sloane_