OFFSET
1,4
COMMENTS
a(m,n) is the sum of all the entries above it plus the sum of all the entries to the left of it plus the sum of all the entries on the northwest diagonal from it.
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened)
Peter Kagey, Parity bitmap of first 1024 rows and columns. (Even and odd entries and represented by black and white pixels respectively.)
FORMULA
a(1,1)=1; a(1,2)=1; a(1,3)=2; a(2,1)=1; a(2,2)=3; a(2,3)=7; a(3,1)=2; a(3,2)=7; a(3,3)=22; a(m,n) = 2*a(m-1,n)+2*a(m,n-1)-a(m-1,n-1)-3*a(m-2,n-1)-3*a(m-1,n-2)+4*a(m-2,n-2), where m >=3 or n >= 3 and a(m,n)=0 if m <= 0 or n <= 0.
G.f.: (xy-x^2y-xy^2+x^3y^2+x^2y^3-x^3y^3)/(1-2x-2y+xy+3x^2y+3xy^2-4x^2y^2).
EXAMPLE
The table begins
1 1 2 4 8 16 32 ...
1 3 7 17 40 92 208 ...
2 7 22 60 158 401 990 ...
4 17 60 188 543 1498 3985 ...
8 40 158 543 1712 5079 14430 ...
a(3,4)=4+17+2+7+22+1+7=60.
CROSSREFS
KEYWORD
AUTHOR
Martin J. Erickson (erickson(AT)truman.edu), Nov 13 2007
STATUS
approved