A137347 Triangular sequence from coefficients of a polynomial recursion: p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3).

1, -1, 1, 0, -1, -1, 0, 0, 1, -2, 0, 0, 0, 2, 1, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 7, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,10

Comments

Row sums are:

{1, 0, -2, -1, 3, 3, -4, -7, 4, 14, -1, -25, -9, 40, 33, -56}

Links

Table of n, a(n) for n=1..117.

Formula

p(x, n] = x*p(x, n - 1) - 2*x^2*p(x, n - 2) + x^3*p(x, n - 3).

Example

{1},
{-1, 1},
{0, -1, -1},
{0, 0, 1, -2},
{0, 0, 0, 2, 1},
{0, 0, 0, 0, -1, 4},
{0, 0, 0, 0, 0, -4},
{0, 0, 0, 0, 0, 0, 0, -7},
{0, 0, 0, 0, 0, 0, 0, 7, -3},
{0, 0, 0, 0, 0, 0, 0, 0, 3, 11},
{0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10},
{0, 0, 0, 0, 0,0, 0, 0, 0, 0, -10, -15},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,15, -24},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 16},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 49},
{0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, -49, -7}

Mathematica

Clear[p, x, a0, b0] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x - 1; p[x_, n_] := p[x, n] = x*p[x, n - 1] - 2*x^2*p[x, n - 2] + x^3*p[x, n - 3]; g = Table[ExpandAll[p[x, n]], {n, 0, 15}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 15}]; Flatten[a]

Crossrefs

Sequence in context: A317636 A305566 A326813 * A024941 A219492 A285796

Adjacent sequences: A137344 A137345 A137346 * A137348 A137349 A137350

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Apr 08 2008

Status

approved