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).

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

Offset

1,2

Comments

R

References

Henry McKean and Victor 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

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: A171244 A028305 A347086 * A087318 A087319 A101348

Adjacent sequences: A137346 A137347 A137348 * A137350 A137351 A137352

Keyword

uned,tabf,sign

Author

Roger L. Bagula, Apr 08 2008

Status

approved