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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
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are:

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

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..27.

FORMULA

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

EXAMPLE

{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}

MATHEMATICA

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}}]

CROSSREFS

Sequence in context: A011218 A171244 A028305 * A087318 A087319 A101348

Adjacent sequences:  A137346 A137347 A137348 * A137350 A137351 A137352

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Apr 08 2008

STATUS

approved

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Last modified August 1 03:52 EDT 2021. Contains 346384 sequences. (Running on oeis4.)