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A112838 Small-number statistic from the enumeration of domino tilings of a 5-pillow of order n. 11
1, 2, 5, 13, 13, 29, 34, 100, 130, 305, 361, 881, 1145, 2906, 3557, 8669, 10693, 26893, 33680, 83360, 102800, 254565, 317165, 790037, 980237, 2428298, 3011265, 7483801, 9301217, 23092857, 28646722, 71093860 (list; graph; refs; listen; history; text; internal format)



A 5-pillow is a generalized Aztec pillow. The 5-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 5 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square.

Plotting A112838(n+2)/A112838(n) gives an intriguing damped sine curve.


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


Table of n, a(n) for n=0..31.


The number of domino tilings of the 5-pillow of order 6 is 1666=7^2*34. A112838(n)=34.


A112833 breaks down as A112834^2 times A112835, where A112835 is not necessarily squarefree.

3-pillows: A112833-A112835; 7-pillows: A112839-A112841; 9-pillows: A112842-A112844.

Sequence in context: A336883 A067365 A189993 * A111296 A089728 A127987

Adjacent sequences:  A112835 A112836 A112837 * A112839 A112840 A112841




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



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Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)