OFFSET
0,5
COMMENTS
Matrix product Q^-1*P^2 = SHIFT_DOWN_RIGHT(Q). Compare to the matrix product Q^2*P^-1 = SHIFT_LEFT_UP(P), as given by triangle A113369.
EXAMPLE
The product Q^-1*P^2 forms a triangle that begins:
1;
0,1;
0,2,1;
0,5,4,1;
0,19,22,6,1;
0,113,166,51,8,1;
0,966,1671,561,92,10,1;
0,10958,21510,7726,1324,145,12,1;
0,156700,341463,129406,23010,2575,210,14,1;
0,2727794,6496923,2572892,471724,53935,4434,287,16,1; ...
Compare Q^-1*P^2 to Q (A113350) which begins:
1;
2,1;
5,4,1;
19,22,6,1;
113,166,51,8,1;
966,1671,561,92,10,1;
10958,21510,7726,1324,145,12,1; ...
PROG
(PARI) T(n, k)=local(A, B); A=matrix(1, 1); A[1, 1]=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^(2*j-1))[i-j+1, 1])); )); A=B); (A^(2*k))[n-k+1, 1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 12 2005
STATUS
approved