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

0,3

Links

Table of n, a(n) for n=0..56.

Example

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.

Sequence in context: A199662 A280293 A226483 * A306938 A257259 A074475

Adjacent sequences: A103404 A103405 A103406 * A103408 A103409 A103410

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 04 2005

Extensions

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

Status

approved