A113394 - OEIS

%I #5 Jun 13 2017 23:30:37

%S 1,9,1,99,18,1,1569,360,27,1,34344,9051,783,36,1,980487,284148,26820,

%T 1368,45,1,34930455,10865358,1089126,59250,2115,54,1,1502349459,

%U 494019714,51784137,2946456,110715,3024,63,1,76058669082,26168502684

%N Triangle, read by rows, equal to the matrix cube of triangle A113389.

%F Column k of A113389^3 = column 0 of A113389^(3*k+3) for k>=0.

%e Triangle A113389^3 begins:

%e 1;

%e 9,1;

%e 99,18,1;

%e 1569,360,27,1;

%e 34344,9051,783,36,1;

%e 980487,284148,26820,1368,45,1;

%e 34930455,10865358,1089126,59250,2115,54,1;

%e 1502349459,494019714,51784137,2946456,110715,3024,63,1;

%e 76058669082,26168502684,2840586075,167137110,6510780,185589,4095,72,1;

%o (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); (matrix(#A,#A,r,c,if(r>=c,(A^(3*c))[r-c+1,1]))^3)[n+1,k+1]

%Y Cf. A113389, A113395 (column 0); recurrence: A091351, A113355.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Nov 14 2005