A270668 Triangle read by rows: The number of domino tilings of the (2n+1) X (2m+1) board with a central free square.

1, 0, 2, 1, 0, 196, 0, 32, 0, 75272, 1, 0, 31329, 0, 599466256, 0, 450, 0, 135663392, 0, 28838245503008, 1, 0, 4941729, 0, 10956424382401, 0, 22463213552677201984, 0, 6272, 0, 233075146752, 0, 5652453608244879872, 0, 123818965842734619629420672

Offset

0,3

Comments

Arrangements obtained by rotations and flips are counted as distinct.

Links

Table of n, a(n) for n=0..35.

R. J. Mathar, A270668: Domino tilings with one monomer in the center

Index entries for sequences related to dominoes

Formula

T(n,0) = A059841(n).

T(2n+1,1) = 2 * A098301(n+1). - Alois P. Heinz, Mar 21 2016

T(2n+1,1) = 2*A189006(2n+1,3)^2. - R. J. Mathar, Mar 22 2016

Conjectured g.f. for column 3: ( -1 -4*x +543*x^2 -6238*x^3 +17032*x^4 -6238*x^5 +543*x^6 -4*x^7 -x^8 ) / ( (x-1) *(x^2-7*x+1) *(x^2-23*x+1) *(x^4 -161*x^3 +576*x^2 -161*x +1) ). - R. J. Mathar, Mar 23 2016

Example

For n=m=1, the 3 X 3 board can be covered in T(1,1)=2 ways, starting in one corner with either a horizontal or a vertical domino.
Triangle begins:
1;
0, 2;
1, 0, 196;
0, 32, 0, 75272;
1, 0, 31329, 0, 599466256;
0, 450, 0, 135663392, 0, 28838245503008;
1, 0, 4941729, 0, 10956424382401, 0, 22463213552677201984;

Crossrefs

Cf. A098301, A143659 (diagonal), A189006 (free square in corner).

Sequence in context: A139037 A108511 A261160 * A196272 A086073 A053622

Adjacent sequences: A270665 A270666 A270667 * A270669 A270670 A270671

Keyword

nonn,tabl

Author

R. J. Mathar, Mar 21 2016

Extensions

More terms from Alois P. Heinz, Mar 21 2016

Status

approved