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

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

Triangle begins:
  {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},
  ...

Mathematica

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,tabf,sign

Author

Roger L. Bagula, Apr 08 2008

Status

approved