%I #10 Jul 13 2018 21:06:41
%S 1,1,2,5,14,42,128,390,1184,3582,10808,32550,97904,294222,883688,
%T 2653110,7963424,23898462,71711768,215168070,645569744,1936840302,
%U 5810783048,17432873430,52299668864,156901103742,470707505528,1412130905190,4236409492784,12709262032782,38127853207208
%N Expansion of 1 + (1/(1-x) + 1/(1-3*x))*x/2 + (1/(1-x) - 8/(1-2*x) + 9/(1-3*x))*x^5/2.
%H Nickolas Hein, Jia Huang, <a href="https://arxiv.org/abs/1807.04623">Nonassociativity measurements of some binary operations</a>, arXiv:1807.04623 [math.CO], 2018. See Proposition 2.10 p. 9 (and line 2, page 6 for the x factor in the g.f.)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n) = 1 + 5*3^(n-3) - 2^(n-3), n>=3.
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3), n>=6.
%t CoefficientList[Series[1 + (1/(1 - x) + 1/(1 - 3 x)) x/2 + (1/(1 - x) - 8/(1 - 2 x) + 9/(1 - 3 x)) x^5/2, {x, 0, 30}], x] (* or *)
%t LinearRecurrence[{6, -11, 6}, {1, 1, 2, 5, 14, 42}, 31] (* _Michael De Vlieger_, Jul 13 2018 *)
%o (PARI) Vec(1 + (1/(1-x) + 1/(1-3*x))*x/2 + (1/(1-x) - 8/(1-2*x) + 9/(1-3*x))*x^5/2 + O(x^40)) \\ _Michel Marcus_, Jul 13 2018
%K nonn,easy
%O 0,3
%A _Michel Marcus_, Jul 13 2018