login
Column 0 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 T.
3

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

%S 1,1,2,6,22,94,446,2294,12542,71974,429342,2643606,16710382,107980870,

%T 710933118,4756345750,32265548622,221540438502,1537355395934,

%U 10768777480374,76063545106670,541277072787334,3877624448977150

%N Column 0 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 T.

%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(A[n+1,1])}

%Y Cf. A109316 (triangle), A109318 (column 1), A109319 (row sums), A000108.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 07 2005