OFFSET
1,2
COMMENTS
Row sums are A004798 (convolution of Fibonacci numbers 1,2,3,5,... with themselves). Central numbers of the rows are A006498 (a(n) = a(n-1)+a(n-3)+a(n-4)). First column and main diagonal are Fibonacci numbers 1,2,3,5,... First subdiagonal are 2*Fibonacci numbers. T(n,k) = F(n-k+2)*F(k+1) where F(m) is the m-th Fibonacci number. For the antidiagonal sums b(n): b(1) = 1, b(2) = 2, then b(n) = b(n-1) + b(n-2) + F(floor((n+3)/2)).
T(n,k) is the number of Boolean intervals of the form [s_k,w] in the weak order on S_n, for a fixed simple reflection s_k. - Bridget Tenner, Jan 16 2020
LINKS
B. E. Tenner, Interval structures in the Bruhat and weak orders, arXiv:2001.05011 [math.CO], 2020.
FORMULA
G.f.: (1+x+y+x*y)/((1-x-x^2)*(1-y-y^2)) [U coordinates] - N. J. A. Sloane, Jun 01 2005
EXAMPLE
Triangle begins
1;
2, 2;
3, 4, 3;
5, 6, 6, 5;
8, 10, 9, 10, 8;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gerald McGarvey, May 28 2005
STATUS
approved