A122374 Triangle in which row n gives the coefficients of det(A-xI), where A is the n X n matrix with 1's on antidiagonal and last row and column, 0's elsewhere.

1, 1, -1, -1, -1, 1, -1, 1, 2, -1, 1, -1, -4, -1, 1, 1, -3, -3, 4, 2, -1, -1, 3, 7, -2, -7, -1, 1, -1, 5, 4, -11, -5, 7, 2, -1, 1, -5, -10, 9, 18, -3, -10, -1, 1, 1, -7, -5, 22, 9, -24, -7, 10, 2, -1, -1, 7, 13, -20, -34, 18, 34, -4, -13, -1, 1, -1, 9, 6, -37, -14, 58, 16, -42, -9, 13, 2, -1, 1, -9, -16, 35, 55, -50, -80, 30, 55, -5, -16, -1, 1

Offset

0,9

Links

Table of n, a(n) for n=0..90.

Example

Triangle starts:
{ 1},
{ 1,  -1},
{-1,  -1,   1},
{-1,   1,   2,  -1},
{ 1,  -1,  -4,  -1,   1},
{ 1,  -3,  -3,   4,   2,  -1},
{-1,   3,   7,  -2,  -7,  -1,   1},
{-1,   5,   4, -11,  -5,   7,   2,  -1},
{ 1,  -5, -10,   9,  18,  -3, -10,  -1,   1},
{ 1,  -7,  -5,  22,   9, -24,  -7,  10,   2,  -1}
...
From M. F. Hasler, Apr 30 2018: (Start)
For n = 0, the determinant of the 0 X 0 matrix is 1 by convention, which yields row 0 = [ 1 ].
For n = 1, we have det [1 - x] = 1 - x, which yields row 1 = [1, -1].
For n = 2, we have det [-x, 1; 1, 1 - x] = x(x - 1) - 1 = x^2 - x - 1; in order of increasing powers this yields row 2 = [-1, -1, +1]. (End)

Prog

(PARI) A122374_row(n)=(-1)^n*Vecrev(charpoly(matrix(n, n, i, j, i==n||j==n||i+j==n+1), x)) \\ Yields the n-th row. - M. F. Hasler, Apr 26 2018

Crossrefs

Sequence in context: A353573 A345000 A352894 * A261960 A010121 A174726

Adjacent sequences: A122371 A122372 A122373 * A122375 A122376 A122377

Keyword

sign,easy,less,tabl

Author

Roger L. Bagula and Gary W. Adamson, Oct 19 2006

Extensions

Edited by M. F. Hasler, Apr 26 2018

Status

approved