OFFSET
0,2
COMMENTS
Complementary to A114151, which gives R^-2*Q^3 = Q^-1*P^2.
EXAMPLE
Triangle R^2*Q^-1 = Q^3*P^-2 begins:
1;
4,1;
28,7,1;
326,91,10,1;
5702,1722,190,13,1;
136724,43764,4945,325,16,1;
4226334,1415799,163705,10751,496,19,1; ...
Compare to P (A113370):
1;
1,1;
1,4,1;
1,28,7,1;
1,326,91,10,1;
1,5702,1722,190,13,1; ...
Thus R^2*Q^-1 = Q^3*P^-2 equals P shift left one column.
PROG
(PARI) T(n, k)=local(P, Q, R, W); P=Mat(1); for(m=2, n+1, W=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, W[i, j]=1, if(j==1, W[i, 1]=1, W[i, j]=(P^(3*j-2))[i-j+1, 1])); )); P=W); Q=matrix(#P, #P, r, c, if(r>=c, (P^(3*c-1))[r-c+1, 1])); R=matrix(#P, #P, r, c, if(r>=c, (P^(3*c))[r-c+1, 1])); (R^2*Q^-1)[n+1, k+1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 15 2005
STATUS
approved