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 A249993 #18 Oct 11 2022 00:52:06
%S A249993 1,1,11,29,147,525,2227,8653,35123,139469,559923,2235597,8950579,
%T A249993 35785933,143176499,572640461,2290692915,9162509517,36650562355,
%U A249993 146601200845,586406900531,2345623407821,9382502019891,37529991302349,150119998763827,600479927946445
%N A249993 Expansion of 1/((1+x)*(1+2*x)*(1-4*x)).
%H A249993 Colin Barker, <a href="/A249993/b249993.txt">Table of n, a(n) for n = 0..1000</a>
%H A249993 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,8).
%F A249993 G.f.: 1/((1+x)*(1+2*x)*(1-4*x)).
%F A249993 a(n) = ( 2^(3+2*n) + (5*2^(1+n) - 3)*(-1)^n )/15. _Colin Barker_, Dec 28 2014
%F A249993 a(n) = a(n-1) + 10*a(n-2) + 8*a(n-3). - _Colin Barker_, Dec 28 2014
%F A249993 E.g.f.: (1/15)*(10*exp(-2*x) - 3*exp(-x) + 8*exp(4*x)). - _G. C. Greubel_, Oct 10 2022
%t A249993 CoefficientList[Series[1/((1+x)(1+2x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{1,10,8},{1,1,11},30] (* _Harvey P. Dale_, Dec 13 2018 *)
%o A249993 (PARI) Vec(1/((1+x)*(1+2*x)*(1-4*x)) + O(x^40)) \\ _Michel Marcus_, Dec 28 2014
%o A249993 (Magma) [(2^(2*n+3) +(-1)^n*(5*2^(n+1)-3))/15: n in [0..40]]; // _G. C. Greubel_, Oct 10 2022
%o A249993 (SageMath) [(2^(2*n+3) +(-1)^n*(5*2^(n+1)-3))/15 for n in range(41)] # _G. C. Greubel_, Oct 10 2022
%Y A249993 Cf. A249992.
%Y A249993 Cf. A006095, A171477 for g.f. 1/((1-x)*(1-2*x)*(1-4*x)).
%Y A249993 Cf. A015249, A084152, A084175 for g.f. 1/((1-x)*(1+2*x)*(1-4*x)).
%Y A249993 Cf. A109765 for g.f. 1/((1+x)*(1-2*x)*(1-4*x)).
%K A249993 nonn,easy
%O A249993 0,3
%A A249993 _Alex Ratushnyak_, Dec 27 2014