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

%I A112830 #8 Nov 30 2015 06:56:31
%S A112830 1,1,5,1,10,25,1,17,65,113,1,26,146,346,481,1,37,292,932,1637,1985,1,
%T A112830 50,533,2248,5013,7218,8065,1,65,905,4937,13897,24201,30529,32513,1,
%U A112830 82,1450,10018,35218,74530,108970,126034,130561,1,101,2216,19016,82436
%N A112830 Table of number of domino tilings of generalized Aztec pillows of type (1, ..., 1, 3, 1, ..., 1)_n.
%C A112830 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).
%H A112830 C. Hanusa, <a href="http://qc.edu/~chanusa/research/papers/Dissertation.pdf">A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows</a>, PhD Thesis, 2005, University of Washington, Seattle, USA.
%F A112830 T(2*n,n) = A264960(n). - _Peter Bala_, Nov 29 2015
%e A112830 The number of tilings of a generalized Aztec pillow of type (1,1,3,1)_n is entry (4,3) = 346.
%p A112830 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)]);
%Y A112830 A092440 (main diagonal), A092441 (first subdiagonal), A002522 (column k = 1), A066455 (column k = 2). Cf. A264960.
%K A112830 easy,nonn,tabl
%O A112830 0,3
%A A112830 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005