A112842 Number of domino tilings of a 9-pillow of order n.

1, 2, 5, 13, 34, 89, 356, 1737, 9065, 49610, 325832, 2795584, 28098632, 310726442, 3877921669, 58896208285, 1083370353616, 22901813128125, 548749450880000, 15471093192996501, 522297110942557556, 20691062026775504896

Offset

0,2

Comments

A 9-pillow is a generalized Aztec pillow. The 9-pillow of order n is a rotationally-symmetric region. It has a 2 X 2n central band of squares and then steps up from this band with steps of 9 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square.

References

C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.

Links

Table of n, a(n) for n=0..21.

Example

The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185.

Crossrefs

A112842 breaks down as A112843^2 times A112844, where A112844 is not necessarily squarefree.

3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 7-pillows: A112839-A112841.

Sequence in context: A122367 A367658 A114299 * A097417 A367657 A006801

Adjacent sequences: A112839 A112840 A112841 * A112843 A112844 A112845

Keyword

nonn

Author

Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005

Status

approved