OFFSET
1,4
COMMENTS
It appears that in the column k, starting in row n, the sum of k successive terms is equal to A000041(n-1).
FORMULA
It appears that A000041(n) = Sum_{j=1..k} T(n+j,k), n >= 0, k >= 1.
EXAMPLE
Array begins:
. 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
. 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
. 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
. 3, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,...
. 5, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,...
. 7, 4, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0,...
. 11, 3, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0,...
. 15, 8, 3, 3, 1, 1, 0, 1, 0, 0, 0, 0,...
. 22, 7, 6, 2, 2, 1, 1, 0, 1, 0, 0, 0,...
. 30, 15, 6, 5, 3, 2, 1, 1, 0, 1, 0, 0,...
. 42, 15, 10, 5, 4, 2, 2, 1, 1, 0, 1, 0,...
. 56, 27, 14, 10, 5, 5, 2, 2, 1, 1, 0, 1,...
...
For n = 7, from the conjecture we have that p(n-1) = p(6) = 11 = 3+8 = 2+3+6 = 1+3+2+5 = 1+1+2+3+4 = 0+1+1+2+2+5, etc. where p(n) = A000041(n).
CROSSREFS
KEYWORD
AUTHOR
Omar E. Pol, Feb 04 2012
STATUS
approved