OFFSET
1,1
EXAMPLE
a(2,.) = 2,4,6,7,9,11,12,13,16,... = sum of two positive triangular numbers = A051533;
a(3,.) = 2,5,8,11,14,20,21,24,30,36,... = sum of two positive tetrahedral numbers;
First antidiagonals of the array are:
2;
2,3;
2,4,4;
2,5,6,5;
...
MATHEMATICA
nMax = 13; coeff = Floor[nMax/2]+1; row[n_] := Table[Binomial[x, n] + Binomial[y, n], {x, n, coeff*n}, {y, n, coeff*n}] // Flatten // Union; A0 = {}; While[A051693 = Table[row[n][[1 ;; nMax]], {n, 1, nMax}]; A051693 =!= A0, A0 = A051693; coeff++]; Table[A051693[[n-k+1, k]], {n, 1, nMax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 14 2016 *)
CROSSREFS
KEYWORD
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
STATUS
approved