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 A195339 #21 Mar 29 2024 05:43:22
%S A195339 1,4,16,62,239,920,3540,13620,52401,201604,775636,2984122,11480879,
%T A195339 44170640,169938680,653808840,2515413201,9677604804,37232862856,
%U A195339 143246816182,551116641919,2120323237160,8157566453420,31384785713660,120747379738401
%N A195339 Expansion of 1/(1-4*x+2*x^3+x^4).
%H A195339 Bruno Berselli, <a href="/A195339/b195339.txt">Table of n, a(n) for n = 0..1000</a>
%H A195339 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-2,-1).
%F A195339 G.f.: 1/((1-x)*(1-3*x-3*x^2-x^3)).
%F A195339 a(n) = 4*a(n-1)-2*a(n-3)-a(n-4).
%t A195339 CoefficientList[Series[1/(1-4x+2x^3+x^4),{x,0,30}],x] (* or *) LinearRecurrence[{4,0,-2,-1},{1,4,16,62},30] (* _Harvey P. Dale_, Dec 02 2011 *)
%o A195339 (PARI) Vec(1/(1-4*x+2*x^3+x^4)+O(x^25))
%o A195339 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-4*x+2*x^3+x^4)));
%o A195339 (Maxima) makelist(coeff(taylor(1/(1-4*x+2*x^3+x^4), x, 0, n), x, n), n, 0, 24);
%Y A195339 Cf. A185962 (gives the coefficients of the denominator of the g.f., row 5 of its triangular array). Sequences likewise related to A185962: A000007 (row 1), A000012 (row 2), A000129 (row 3) and A006190 (row 4).
%K A195339 nonn,easy
%O A195339 0,2
%A A195339 _Bruno Berselli_, Sep 16 2011