OFFSET
0,2
COMMENTS
Leftmost column is A082164 (enumerates acyclic automata with 3 inputs). The operation SHIFTUP(T) shifts each column of T up 1 row, dropping the elements that occupied the diagonal of T.
FORMULA
EXAMPLE
Rows of T begin:
[1],
[7,2],
[133,26,3],
[5362,962,63,4],
[380093,66794,3843,124,5],
[42258384,7380100,409248,11284,215,6],
[6830081860,1190206134,65160081,1709836,27305,342,7],...
Rows of T^2 begin:
[1],
[21,4],
[714,130,9],
[41923,7410,441,16],...
Rows of T^3 begin:
[1],
[49,8],
[2821,494,27],
[238238,41678,2331,64],...
Rows of T^3 + 3*T^2 + 3*T equals SHIFTUP(T):
[7],
[133,26],
[5362,962,63],
[380093,66794,3843,124],...
PROG
(PARI) {T(n, k)=local(P, D); D=matrix(n+1, n+1, r, c, if(r==c, r)); P=matrix(n+1, n+1, r, c, if(r>=c, (-1)^(r-c)*(c^3+3*c^2+3*c)^(r-c)/(r-c)!)); return(if(n<k||k<0, 0, (P*D*P^-1)[n+1, k+1]))}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jan 31 2005
STATUS
approved