A341830 Irregular triangle read by rows: the n-th row gives the y-values of the solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.

2, 3, 4, 3, 5, 4, 6, 4, 5, 7, 6, 8, 5, 7, 9, 8, 10, 6, 9, 11, 10, 12, 5, 7, 11, 13, 12, 14, 6, 8, 13, 15, 6, 14, 16, 7, 9, 15, 17, 16, 18, 7, 8, 10, 17, 19, 18, 20, 9, 11, 19, 21, 8, 20, 22, 10, 12, 21, 23, 22, 24, 7, 9, 11, 13, 23, 25, 24, 26, 12, 14, 25, 27, 8, 10, 26, 28

Offset: 1

Author

Stefano Spezia, Feb 21 2021

Keywords

• nonn
• tabf

Comments

Equivalently, the n-th row gives the row indices corresponding to 2*n + 1 in the triangle A340804.

Examples

			Triangle begins:
   2
   3
   4
   3   5
   4   6
   4   5   7
   6   8
   5   7   9
   8  10
   6   9  11
  10  12
   5   7  11  13
  12  14
   6   8  13  15
   6  14  16
   7   9  15  17
  16  18
   7   8  10  17  19
  ...
		

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10175 (first 1500 rows of the triangle, flattened).

Crossrefs

Cf. A005843, A340804, A340805 (row length or solutions number), A341829 (x-values).

Programs

Mathematica

Table[Union[n/Intersection[Divisors[n],Table[d,{d,Floor[(1+Sqrt[1+8n])/4]}]]+1,n/Intersection[Divisors[n],Table[d,{d,Floor[(Sqrt[1+2n]-1)/2]}]]-1],{n,27}]//Flatten