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%I #17 Apr 21 2022 14:02:09
%S 0,0,0,1,2,8,18,53,124,328,780,1969,4718,11648,28014,68405,164824,
%T 400240,965304,2337409,5640122,13637336,32914794,79525973,191966740,
%U 463636600,1119239940,2702647921,6524535782,15753313808,38031163398
%N a(n) = 2*a(n-1) + 4*a(n-2) - 6*a(n-3) - 3*a(n-4).
%C Based on a Pell recurrence.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-6,-3).
%H G. C. Greubel, <a href="/A136201/a136201.txt">Table of n, a(n) for n = 0..1000</a>
%F A137255(n+1) - 2*A137255(n), same recurrence.
%F a(n) = (-A108411(n) + A001333(n))/4. - _R. J. Mathar_, Apr 01 2008
%F a(n) = (1/8)*(1+sqrt(2))^n + (1/8)*(1-sqrt(2))^n + (1/24)*3^(n/2)*(-3 - sqrt(3) - 3(-1)^n + (-1)^n*sqrt(3)). - _Emeric Deutsch_, Mar 31 2008
%F G.f.: x^3/(3*x^4 + 6*x^3 - 4*x^2 - 2*x + 1). - _Alexander R. Povolotsky_, Mar 31 2008
%p a:=proc(n) options operator, arrow: expand((1/8)*(1+sqrt(2))^n+(1/8)*(1-sqrt(2))^n+(1/24)*3^((1/2)*n)*(-3-sqrt(3)-3*(-1)^n+(-1)^n*sqrt(3))) end proc: seq(a(n),n=0..30); # _Emeric Deutsch_, Mar 31 2008
%t LinearRecurrence[{2, 4, -6, -3}, {0, 0, 0, 1}, 50] (* _G. C. Greubel_, Feb 23 2017 *)
%t CoefficientList[Series[x^3/(1-2 x-4 x^2+6 x^3+3 x^4),{x,0,50}],x] (* _Harvey P. Dale_, Apr 21 2022 *)
%o (PARI) x='x+O('x^50); Vec(x^3/(3*x^4 + 6*x^3 - 4*x^2 - 2*x + 1)) \\ _G. C. Greubel_, Feb 23 2017
%K nonn,easy
%O 0,5
%A _Paul Curtz_, Mar 16 2008
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