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A342907
a(n) is the number of tilings of the order-n Aztec Diamond by square tetrominoes and Z-shaped tetrominoes, counting all rotations and reflections as distinct.
1
1, 4, 20, 304, 6784, 407684, 39072966, 9449433606, 3830070645700, 3762885306351756, 6402694828334379856, 25695884677997378383120
OFFSET
1,2
COMMENTS
Computed by Don Reble, Mar 31 2021; a(8) from Mike Beeler, Mar 31 2021; a(9) from Walter Trump, Apr 01 2021
Comments from Allan C. Wechsler, Mar 31 2021: (Start)
Motivated by a query from James Propp in the Math-Fun forum, Mar 28 2021.
An Aztec Diamond of order n is a set of squares whose centers are at distance n or closer to a vertex in the taxicab metric.
Tilings by dominoes are counted by A006125. (End)
LINKS
James Propp, A Pedestrian Approach to a Method of Conway, or, A Tale of Two Cities, Mathematics Magazine, Vol. 70, No. 5 (Dec., 1997), 327-340.
CROSSREFS
Cf. A006125.
Sequence in context: A362259 A120599 A012797 * A358544 A167002 A227005
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Mar 31 2021
EXTENSIONS
a(10) from Andrew Howroyd, Apr 01 2021
a(11) from Walter Trump, Apr 06 2021
a(12) from Bert Dobbelaere, May 21 2021
STATUS
approved