OFFSET
0,5
COMMENTS
Complementary to A114152, which gives R^3*P^-1.
EXAMPLE
Triangle R^-1*P^3 begins:
1;
0,1;
0,6,1;
0,48,12,1;
0,605,186,18,1;
0,11196,3892,414,24,1;
0,280440,106089,12021,732,30,1; ...
Compare to R^2 (A113392):
1;
6,1;
48,12,1;
605,186,18,1;
11196,3892,414,24,1;
280440,106089,12021,732,30,1; ...
Thus R^-1*P^3 equals R^2 shift right 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^-1*P^3)[n+1, k+1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 15 2005
STATUS
approved