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 A137349 A triangular sequence from coefficients of a mixed type of three deep polynomial recursion: Q(x, n) = 6*x*Q(x, n - 2)*Q(x, n - 3) - 2*Q(x, n - 3). 0

%I

%S 1,-2,2,0,-2,-12,12,4,-4,0,4,-24,-264,576,-288,-8,8,0,-8,-144,1872,

%T 10368,-39744,41472,-13824,16,-16

%N A triangular sequence from coefficients of a mixed type of three deep polynomial recursion: Q(x, n) = 6*x*Q(x, n - 2)*Q(x, n - 3) - 2*Q(x, n - 3).

%C Row sums are:

%C {1, 0, 0, -2, 0, 0, 4, 0, 0, -8, 0}

%C This polynomial recursion was suggested by the soliton equation ( Korteweg and de Vries) in McKean and Moll, but is my own idea.

%D McKean and Moll, Elliptic Curves, Function Theory,Geometry, Arithmetic, Cambridge University Press, New York, 1997, page 91

%F Q(x, n) = 6*x*Q(x, n - 2)*Q(x, n - 3) - 2*Q(x, n - 3).

%e {1},

%e {-2, 2},

%e {0},

%e {-2, -12, 12},

%e {4, -4},

%e {0},

%e {4, -24, -264, 576, -288},

%e {-8, 8},

%e {0},

%e {-8, -144, 1872, 10368, -39744, 41472, -13824},

%e {16, -16}

%t Clear[Q, x] Q[x, -2] = 1 - x; Q[x, -1] = 0; Q[x, 0] = 1; Q[x_, n_] := Q[x, n] = 6*x*Q[x, n - 2]*Q[x, n - 3] - 2*Q[x, n - 3] Table[ExpandAll[Q[x, n]], {n, 0, 10}] a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}] (* here I had to add {0} for null {} to get a representation*) Flatten[{{1}, {-2, 2}, {0}, {-2, -12, 12}, {4, -4}, {0}, {4, -24, -264, 576, -288}, {-8, 8}, {0}, {-8, -144, 1872, 10368, -39744, 41472, -13824}, {16, -16}}]

%K uned,tabl,sign

%O 1,2

%A _Roger L. Bagula_, Apr 08 2008

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Last modified September 25 15:27 EDT 2021. Contains 347658 sequences. (Running on oeis4.)