%I A113378
%S A113378 1,3,1,15,12,1,136,168,21,1,1998,3190,483,30,1,41973,80136,13615,960,39,
%T A113378 1,1166263,2553162,469476,35785,1599,48,1,40747561,99579994,19419225,
%U A113378 1562220,74074,2400,57,1,1726907675,4624245724,944233801,79072620
%N A113378 Triangle, read by rows, equal to the matrix cube of A113370.
%F A113378 Column k of A113370^3 = column 0 of A113389^(3*k+1) for k>=0.
%e A113378 Triangle A113370^3 begins:
%e A113378 1;
%e A113378 3,1;
%e A113378 15,12,1;
%e A113378 136,168,21,1;
%e A113378 1998,3190,483,30,1;
%e A113378 41973,80136,13615,960,39,1;
%e A113378 1166263,2553162,469476,35785,1599,48,1;
%e A113378 40747561,99579994,19419225,1562220,74074,2400,57,1;
%e A113378 1726907675,4624245724,944233801,79072620,3908034,132856,3363,66,1;
%o A113378 (PARI) {T(n,k)=local(A,B);A=Mat(1);for(m=2,n+1,B=matrix(m,m); for(i=1,
               m, for(j=1,i,if(i<3|j==i|j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(3*j-2))[i-j+1,
               1]));));A=B);(A^3)[n+1,k+1]}
%Y A113378 Cf. A113370, A113389, A113379 (column 0), A113380 (column 1).
%Y A113378 Sequence in context: A130757 A014621 A144006 this_sequence A156289 A095922 
               A089278
%Y A113378 Adjacent sequences: A113375 A113376 A113377 this_sequence A113379 A113380 
               A113381
%K A113378 nonn,tabl
%O A113378 0,2
%A A113378 Paul D. Hanna (pauldhanna(AT)juno.com), Nov 14 2005