OFFSET
1,2
COMMENTS
FORMULA
From Yu-Sheng Chang, Jun 05 2020: (Start)
O.g.f.: F(z,v) = -(v^2*z^3+v*z^3-3*v*z^2+1)/((v*z^2-v*z-z+1)^2*(v*z^2-1)*(z-1)*(v*z-1)).
T(n,k) = [v^k] 1/2*n^2*(v^(n+2)+1)/(1-v)^2+1/2*n*(3*v^(n+3)-7*v^(n+2)+7*v-3)/(-1+v)^3-1/2*v*((1-v^(1/2))^4*(-1)^n+(1+v^(1/2))^4)*v^(1/2*n)/(1-v)^4+(6*v^2+6*v^(n+2)+v^(n+4)-3*v^(n+3)-3*v+1)/(1-v)^4.
(End)
EXAMPLE
Northwest corner:
1....3....6....10....15
3....7....13...21....31
6....13...22...34....49
10...21...34...50....70
MAPLE
A := proc(n, k) option remember; ## n >= 0 and k = 0 .. n
if k < 0 or k > n then
0
elif n = 0 then
1
else
A(n-1, k) + A(n-1, k-1) - A(n-2, k-1) + max(n-k+1, k+1)
end if
end proc: # Yu-Sheng Chang, Jun 05 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 07 2011
STATUS
approved