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