A226304 Irregular triangle read by rows: coefficients of certain polynomials P_n(x) arising in the enumeration of tatami mat coverings.

1, 1, 2, 1, 1, 2, 1, 1, 2, 4, 0, 2, 1, 0, 1, 2, 2, -2, 2, 1, 0, 1, 2, 2, 4, -2, 4, 0, 2, -2, 2, 1, 0, 1, 1, 2, 3, 4, -2, 2, 0, 4, -2, 2, -2, 2, 1, 0, 1, 1, 2, 3, 4, 6, -2, 6, 0, 8, -2, 4, -4, 6, -2, 4, -2, 2, -2, 2, 1, -1, 1, 0, 1, 1, 1, 2, 2, -6, 6, -2, 6, -6, 4, -4, 6, -6, 6, -4, 4, -4, 2, 1, -1, 1, 0, 1, 1, 1, 2, 2, 4, -8, 10, -4, 10, -8, 8, -8, 10, -10, 12, -8, 10, -12, 10, -6, 6, -6, 6, -4, 4, -4, 2

Offset

2,3

Comments

See Erickson-Ruskey for precise definition. The polynomials P_n(x) are described as "mysterious".

Links

Table of n, a(n) for n=2..124.

Alejandro Erickson, Frank Ruskey, Enumerating maximal tatami mat coverings of square grids with v vertical dominoes, arXiv:1304.0070 [math.CO], 2013.

Example

Triangle begins:
1
1,2
1,1,2
1,1,2,4,0,2
1,0,1,2,2,-2,2
1,0,1,2,2,4,-2,4,0,2,-2,2
1,0,1,1,2,3,4,-2,2,0,4,-2,2,-2,2
1,0,1,1,2,3,4,6,-2,6,0,8,-2,4,-4,6,-2,4,-2,2,-2,2
1,-1,1,0,1,1,1,2,2,-6,6,-2,6,-6,4,-4,6,-6,6,-4,4,-4,2
1,-1,1,0,1,1,1,2,2,4,-8,10,-4,10,-8,8,-8,10,-10,12,-8,10,-12,10,-6,6,-6,6,-4,4,-4,2
...

Crossrefs

Cf. A226302, A226303.

Sequence in context: A136610 A377365 A326371 * A101022 A241153 A213852

Adjacent sequences: A226301 A226302 A226303 * A226305 A226306 A226307

Keyword

sign,tabf

Author

N. J. A. Sloane, Jun 06 2013

Status

approved