A103407 Triangle of absolute values of the coefficients (in descending powers) of the characteristic polynomials of n X n matrices with 3's on the main diagonal and 1's elsewhere.

1, 1, 3, 1, 6, 8, 1, 9, 24, 20, 1, 12, 48, 80, 48, 1, 15, 80, 200, 240, 112, 1, 18, 120, 400, 720, 672, 256, 1, 21, 168, 700, 1680, 2352, 1792, 576, 1, 24, 224, 1120, 3360, 6272, 7168, 4608, 1280, 1, 27, 288, 1680, 6048, 14112, 21504, 20736, 11520, 2816, 1, 30

Offset: 0

Author

Gary W. Adamson, Feb 04 2005

Keywords

• nonn
• tabl

Examples

			3rd row (1, 9, 24, 20) with alternating signs = characteristic polynomial 3 X 3 matrix [3 1 1 / 1 3 1 / 1 1 3], x^3 - 9x^2 + 24x - 20.
		

Crossrefs

Row sums are A006234: 1, 4, 15, 54, 189... Rightmost terms in each row = A001792: 1, 3, 8, 20, 48, 112, 256...(row sums of A103406, the analogous triangle with all 2's in the generating matrix.)

See A103247 for another version.

Extensions

Extended and edited by John W. Layman, Mar 17 2005