A112830 Table of number of domino tilings of generalized Aztec pillows of type (1, ..., 1, 3, 1, ..., 1)_n.

1, 1, 5, 1, 10, 25, 1, 17, 65, 113, 1, 26, 146, 346, 481, 1, 37, 292, 932, 1637, 1985, 1, 50, 533, 2248, 5013, 7218, 8065, 1, 65, 905, 4937, 13897, 24201, 30529, 32513, 1, 82, 1450, 10018, 35218, 74530, 108970, 126034, 130561, 1, 101, 2216, 19016, 82436

Offset: 0

Author

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

Keywords

• easy
• nonn
• tabl

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).

Examples

			The number of tilings of a generalized Aztec pillow of type (1,1,3,1)_n is entry (4,3) = 346.
		

Links

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

Crossrefs

A092440 (main diagonal), A092441 (first subdiagonal), A002522 (column k = 1), A066455 (column k = 2). Cf. A264960.

Programs

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)]);

Formula

T(2*n,n) = A264960(n). - Peter Bala, Nov 29 2015