Define an array as follows: b(i,0)=b(0,j)=1, b(i,j)=2*b(i-1,j-1)+b(i-1,j)+b(i,j-1). Then a(n)=b(n,n).
1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544, 98365972, 700701808
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Fri Feb 18 14:28:55 CET 2011 [seqfan] More results on Basket Weave tiling paths