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Row sums of triangle T=A109316 where T(n,k) = [T^2](n-1,k) + [T^2](n-2,k-1) and T^2 is the matrix square of A109316.
3

%I #5 Mar 30 2012 18:36:49

%S 1,2,5,15,55,235,1119,5775,31663,182087,1087927,6706823,42433735,

%T 274403575,1807700679,12099813111,82113733447,563992581079,

%U 3914861387495,27429176467703,193781828188615,1379223584026967

%N Row sums of triangle T=A109316 where T(n,k) = [T^2](n-1,k) + [T^2](n-2,k-1) and T^2 is the matrix square of A109316.

%o (PARI) {a(n)=local(A=Mat(1),B);for(m=1,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(j==i,B[i,j]=1,if(i==2,B[i,j]=1, B[i,j]=(A^2)[i-1,j]+if(j>1,(A^2)[i-2,j-1])));));A=B); return(sum(k=0,n,A[n+1,k+1]))}

%Y Cf. A109316 (triangle), A109317 (column 0), A109318 (column 2).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 07 2005