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A270668 Triangle read by rows: The number of domino tilings of the (2n+1) X (2m+1) board with a central free square. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 14:15 EDT 2019. Contains 324325 sequences. (Running on oeis4.)