A112841 Small-number statistic from the enumeration of domino tilings of a 7-pillow of order n.

1, 2, 5, 13, 34, 34, 74, 73, 193, 256, 793, 1049, 2465, 2857, 6577, 8226, 21348, 28872, 74740, 91970, 222217, 268769, 669265, 852305, 2201945, 2805760, 7000777, 8636081, 21311098, 26588770, 67091170, 85150213

Offset

0,2

Comments

A 7-pillow is a generalized Aztec pillow. The 7-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 7 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square.

Plotting A112841(n+2)/A112841(n) gives an intriguing damped sine curve.

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..31.

Example

The number of domino tilings of the 7-pillow of order 8 is 23353=11^2*193. A112841(n)=193.

Crossrefs

A112839 breaks down as A112840^2 times A112841, where A112841 is not necessarily squarefree.

3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 9-pillows: A112842-A112844.

Sequence in context: A278134 A271940 A273721 * A104589 A154101 A122024

Adjacent sequences: A112838 A112839 A112840 * A112842 A112843 A112844

Keyword

easy,nonn

Author

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

Status

approved