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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.
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%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