OFFSET
0,5
FORMULA
T(n, k) = A113983(n+1, k) - T(n, k-1).
EXAMPLE
Triangle T begins:
1;
1,1;
1,2,1;
1,4,3,1;
1,8,9,4,1;
1,18,27,16,5,1;
1,46,89,64,25,6,1;
1,136,327,276,125,36,7,1;
1,464,1353,1304,665,216,49,8,1;
1,1818,6303,6808,3825,1366,343,64,9,1;
1,8122,32953,39320,23977,9246,2513,512,81,10,1; ...
where A113983(n+1,k) = T(n,k) + T(n,k-1):
A113983(6,3) = 43 = T(5,3) + T(5,2) = 16 + 27;
A113983(7,3) = 153 = T(6,3) + T(6,2) = 64 + 89;
A113983(8,3) = 603 = T(7,3) + T(7,2) = 276 + 327.
PROG
(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==1 || j==i, B[i, j]=1, B[i, j]=A[i-1, j-1]+(A^2)[i-2, j-1] ); )); A=B); (A^(k+1))[n-k+1, 1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 12 2005
STATUS
approved