OFFSET
0,5
COMMENTS
FORMULA
EXAMPLE
Triangle T begins:
1;
1,1;
1,2,1;
1,3,3,1;
1,5,7,4,1;
1,9,17,13,5,1;
1,19,45,43,21,6,1;
1,47,135,153,89,31,7,1;
1,137,463,603,401,161,43,8,1;
1,465,1817,2657,1969,881,265,57,9,1;
1,1819,8121,13111,10633,5191,1709,407,73,10,1;
1,8123,41075,72273,63297,33223,11759,3025,593,91,11,1; ...
Matrix square, T^2 (=A113987), begins:
1;
2,1;
4,4,1;
8,12,6,1;
18,36,26,8,1;
46,116,108,46,10,1;
136,416,468,248,72,12,1; ...
where T(n,k) = T(n-1,k-1) + [T^2](n-2,k-1):
T(8,2) = 463 = T(7,1) + [T^2](6,1) = 47 + 416;
T(8,3) = 603 = T(7,2) + [T^2](6,2) = 135 + 468;
T(8,4) = 401 = T(7,3) + [T^2](6,3) = 153 + 248.
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[n+1, k+1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 12 2005
STATUS
approved