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.

A112839 Number of domino tilings of a 7-pillow of order n.

Original entry on oeis.org

1, 2, 5, 13, 34, 136, 666, 3577, 23353, 200704, 2062593, 24878084, 373006265, 6917185552, 153624835953, 4155902941554, 138450383756352, 5602635336941568, 274540864716936000, 16486029239132118530, 1209110712606533552257
Offset: 0

Views

Author

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

Keywords

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.

Examples

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

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

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.

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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.

Examples

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

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

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.
Showing 1-2 of 2 results.

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