OFFSET
0,3
COMMENTS
The number of tilings of a generalized Aztec pillow of type (k 1's followed by a 3 followed by n-k-1 1's) is entry (n,k+1).
LINKS
C. Hanusa, A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows, PhD Thesis, 2005, University of Washington, Seattle, USA.
FORMULA
T(2*n,n) = A264960(n). - Peter Bala, Nov 29 2015
EXAMPLE
The number of tilings of a generalized Aztec pillow of type (1,1,3,1)_n is entry (4,3) = 346.
MAPLE
matrix(11, 11, [seq([seq(((2^n-sum(binomial(n, j), j=0..k))^2+(binomial(n-1, k))^2)/2, n=k+1..k+11)], k=0..10)]);
CROSSREFS
KEYWORD
AUTHOR
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
STATUS
approved