OFFSET
0,5
COMMENTS
First negative term occurs in the 17th row.
FORMULA
EXAMPLE
Rows begin:
[1],
[1,1],
[1,2,2],
[1,3,3,3],
[1,4,5,5,7],
[1,5,8,8,10,8],
[1,6,12,13,15,15,15],
[1,7,17,21,23,25,23,19],
[1,8,23,33,36,40,38,34,37],
[1,9,30,50,57,63,63,57,56,42],
[1,10,38,73,90,99,103,95,90,79,66],
[1,11,47,103,140,156,166,158,147,135,108,76],
[1,12,57,141,213,246,265,261,242,225,187,142,122],...
Row sums are: {1,2,5,10,22,40,77,136,250,428,744,...}
and form the self-convolution of the antidiagonal sums, which begin: {1,1,2,3,6,8,14,20,35,49,77,112,176,...}.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(k==0 || n<=1, 1, if(n>k, T(n-1, k)+T(n-2, k-1), polcoeff(Ser(vector(n+1, j, sum(i=0, j-1, T(j-i-1, i))))^2+x*O(x^n), n) -sum(i=0, n-1, T(n, i)) )))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jul 26 2004
STATUS
approved