A051693 Square array read by antidiagonals: a(n,k) = sum of two positive regular n-polytopic numbers (i.e., a(n,k) = binomial(x,n) + binomial(y,n) for some x,y >= n).

2, 2, 3, 2, 4, 4, 2, 5, 6, 5, 2, 6, 8, 7, 6, 2, 7, 10, 11, 9, 7, 2, 8, 12, 16, 14, 11, 8, 2, 9, 14, 22, 20, 20, 12, 9, 2, 10, 16, 29, 27, 30, 21, 13, 10, 2, 11, 18, 37, 35, 42, 36, 24, 16, 11, 2, 12, 20, 46, 44, 56, 57, 40, 30, 18, 12, 2, 13, 22, 56, 54, 72, 85, 62, 50, 36, 20, 13, 2

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)

Keywords

• nice
• nonn
• tabl

Examples

			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;
...
		

Crossrefs

Cf. A051533.

Programs

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 *)