A316779 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.

1, 1, 2, 5, 14, 42, 128, 390, 1184, 3582, 10808, 32550, 97904, 294222, 883688, 2653110, 7963424, 23898462, 71711768, 215168070, 645569744, 1936840302, 5810783048, 17432873430, 52299668864, 156901103742, 470707505528, 1412130905190, 4236409492784, 12709262032782, 38127853207208

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Nickolas Hein, Jia Huang, Nonassociativity measurements of some binary operations, 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.)

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

a(n) = 1 + 5*3^(n-3) - 2^(n-3), n>=3.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3), n>=6.

Mathematica

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 *)
LinearRecurrence[{6, -11, 6}, {1, 1, 2, 5, 14, 42}, 31] (* Michael De Vlieger, Jul 13 2018 *)

Prog

(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

Crossrefs

Sequence in context: A148326 A148327 A092493 * A344571 A148328 A290134

Adjacent sequences: A316776 A316777 A316778 * A316780 A316781 A316782

Keyword

nonn,easy

Author

Michel Marcus, Jul 13 2018

Status

approved