%I #5 Jun 13 2017 02:03:30
%S 1,1,1,2,2,1,6,6,2,1,22,22,8,2,1,94,94,36,8,2,1,446,446,176,40,8,2,1,
%T 2294,2294,920,216,40,8,2,1,12542,12542,5080,1224,224,40,8,2,1,71974,
%U 71974,29336,7200,1328,224,40,8,2,1,429342,429342,175752,43712,8160
%N Triangle T, read by rows, where T(n,k) = [T^2](n-1,k) + [T^2](n-2,k-1) (n>k>0), with T(n,0) = [T^2](n-1,0) (n>0) and T(n,n) = 1 (n>=0), where T^2 is the matrix square of T.
%C Limit of rows read backwards = {1,2,8,40,224,...,2^n*A000108(n),...} where A000108(n) = C(2n,n)/(n+1) is the n-th Catalan number.
%e Triangle T begins:
%e 1;
%e 1,1;
%e 2,2,1;
%e 6,6,2,1;
%e 22,22,8,2,1;
%e 94,94,36,8,2,1;
%e 446,446,176,40,8,2,1;
%e 2294,2294,920,216,40,8,2,1;
%e 12542,12542,5080,1224,224,40,8,2,1;
%e 71974,71974,29336,7200,1328,224,40,8,2,1; ...
%e Matrix square T^2 starts:
%e 1;
%e 2,1;
%e 6,4,1;
%e 22,16,4,1;
%e 94,72,20,4,1;
%e 446,352,104,20,4,1;
%e 2294,1848,568,112,20,4,1; ...
%e where T(n,k) = [T^2](n-1,k) + [T^2](n-2,k-1):
%e T(5,2) = [T^2](4,2) + [T^2](3,1) = 20 + 16 = 36;
%e T(7,3) = [T^2](6,3) + [T^2](5,2) = 112 + 104 = 216.
%o (PARI) T(n,k)=local(M=matrix(n,n,r,c,if(r>=c,T(r-1,c-1)))); if(n<k || k<0,0,if(n==k || n<=1,1,(M^2)[n,k+1]+if(k>0,(M^2)[n-1,k])))
%Y Cf. A109317 (column 0), A109318 (column 1), A109319 (row sums), A000108.
%K nonn,tabl
%O 0,4
%A _Paul D. Hanna_, Jul 07 2005
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