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 A112833 Number of domino tilings of a 3-pillow of order n. 20
 1, 2, 5, 20, 117, 1024, 13357, 259920, 7539421, 326177280, 21040987113, 2024032315968, 290333133984905, 62102074862600192, 19808204598680574457, 9421371079480456587520, 6682097668647718038428569, 7067102111711681259234263040, 11145503882824383823706372042925 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A 3-pillow is also called an Aztec pillow. The 3-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 3 horizontal squares to every 1 vertical square and steps down with steps of 1 horizontal square to every 1 vertical square. a(n)^(1/n^2) tends to 1.2211384384439007690866503099... - Vaclav Kotesovec, May 19 2020 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 C. Hanusa, A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows, PhD Thesis, 2005, University of Washington, Seattle, USA. EXAMPLE The number of domino tilings of the 3-pillow of order 4 is 117=3^2*13. MAPLE with(LinearAlgebra): b:= proc(x, y, k) option remember;       `if`(y>x or y Matrix(n, (i, j)-> b(i-1, i-1, j-1)): R:= n-> Matrix(n, (i, j)-> `if`(i+j=n+1, 1, 0)): a:= n-> Determinant(P(n)+R(n).(P(n)^(-1)).R(n)): seq(a(n), n=0..20);  # Alois P. Heinz, Apr 26 2013 MATHEMATICA b[x_, y_, k_] := b[x, y, k] = If[y>x || y

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Last modified July 25 20:55 EDT 2021. Contains 346291 sequences. (Running on oeis4.)