OFFSET
0,5
EXAMPLE
Triangle begins:
1;
1,1;
1,4,1;
1,22,7,1;
1,157,61,10,1;
1,1372,601,118,13,1;
1,14008,6595,1495,193,16,1;
1,161995,79981,20206,3001,286,19,1;
1,2079994,1065589,291394,48685,5281,397,22,1;
1,29268778,15495415,4492621,825313,100456,8497,526,25,1; ...
where diagonals are generated by row polynomials:
T(6,5) = (1) + (1)*(3*5) = 16.
T(6,4) = (1) + (4)*(3*4) + (1)*(3*4)^2 = 193.
T(6,3) = (1) + (22)*(3*3) + (7)*(3*3)^2 + (1)*(3*3)^3 = 1495.
T(6,2) = (1) + (157)*(3*2) + (61)*(3*2)^2 + (10)*(3*2)^3 + (1)*(3*2)^4 = 6595.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k || k==0, 1, sum(j=0, n-k, T(n-k, j)*(3*k)^j)))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 08 2005
STATUS
approved