cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A112844 Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n.

Original entry on oeis.org

1, 2, 5, 13, 34, 89, 89, 193, 185, 410, 482, 1444, 2018, 6362, 8461, 19885, 22861, 51125, 59792, 146749, 195749, 529114, 730465, 1907545, 2350177, 5638489, 6692337, 16167545, 20091490, 51762100, 67753160, 178151440, 229118152
Offset: 0

Views

Author

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

Keywords

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.
Plotting A112844(n+2)/A112844(n) gives an intriguing damped sine curve.

Examples

			The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185. A112844(n)=185.

References

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

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.

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

Original entry on oeis.org

1, 2, 5, 13, 34, 89, 356, 1737, 9065, 49610, 325832, 2795584, 28098632, 310726442, 3877921669, 58896208285, 1083370353616, 22901813128125, 548749450880000, 15471093192996501, 522297110942557556, 20691062026775504896
Offset: 0

Views

Author

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

Keywords

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.

Examples

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

References

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

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.
Showing 1-2 of 2 results.

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