A361442 Infinite triangle T(n, k), n, k >= 0, read and filled by rows the greedy way with distinct integers such that for any n, k >= 0, T(n, k) + T(n+1, k) + T(n+1, k+1) = 0; each term is minimal in absolute value and in case of a tie, preference is given to the positive value.

0, 1, -1, 2, -3, 4, 3, -5, 8, -12, 5, -8, 13, -21, 33, 6, -11, 19, -32, 53, -86, -2, -4, 15, -34, 66, -119, 205, 9, -7, 11, -26, 60, -126, 245, -450, 10, -19, 26, -37, 63, -123, 249, -494, 944, 7, -17, 36, -62, 99, -162, 285, -534, 1028, -1972

Offset: 0

Author

Rémy Sigrist, Mar 12 2023

Keywords

• sign
• tabl

Comments

Will every integer appear in the triangle?

Examples

			Triangle begins:
                             0
                          1     -1
                       2     -3    4
                    3     -5    8    -12
                 5     -8    13   -21    33
              6    -11    19   -32    53   -86
           -2    -4    15   -34    66   -119  205
        9     -7    11   -26    60   -126  245   -450
     10   -19    26   -37    63   -123  249   -494  944
  7    -17    36   -62    99   -162  285   -534  1028 -1972
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010
• Rémy Sigrist, Colored representation of the first 500 rows (the color is function of the sign of T(n, k))
• Rémy Sigrist, PARI program

Crossrefs

Cf. A152920, A361443.

Programs

PARI

See Links section.

Formula

T(n, 0) = A361443(n).

T(n, k) = (-1)^k * Sum_{i = 0..k} binomial(k, i) * T(n-i, 0).