A066201 Array read by antidiagonals upwards: for n-th row (n>=0), T(n,0) = 1; for k > 0, T(n,k) = T(n,k-1)-(n+k-1) if this is positive and has not already appeared in this row, otherwise T(n,k) = T(n,k-1)+(n+k-1).

1, 1, 1, 1, 2, 2, 1, 3, 4, 4, 1, 4, 6, 7, 7, 1, 5, 8, 2, 3, 3, 1, 6, 10, 3, 7, 8, 8, 1, 7, 12, 4, 9, 13, 14, 14, 1, 8, 14, 5, 11, 2, 20, 21, 21, 1, 9, 16, 6, 13, 3, 10, 12, 13, 13, 1, 10, 18, 7, 15, 4, 12, 19, 21, 22, 22, 1, 11, 20, 8, 17, 5, 14, 2, 29, 11, 12, 12

Offset: 0

Author

N. J. A. Sloane, Dec 16 2001

Keywords

• nonn
• easy
• tabl
• look

Examples

			Array begins
   1, 1,  2, 4,  7,  3,  8, 14, 21, 13, ...
   1, 2,  4, 7,  3,  8, 14, 21, 13, 22, ...
   1, 3,  6, 2,  7, 13, 20, 12, 21, 11, ...
   1, 4,  8, 3,  9,  2, 10, 19, 29, 18, ...
   1, 5, 10, 4, 11,  3, 12,  2, 13, 25, ...
   1, 6, 12, 5, 13,  4, 14,  3, 15,  2, ...
   1, 7, 14, 6, 15,  5, 16,  4, 17,  3, ...
   1, 8, 16, 7, 17,  6, 18,  5, 19,  4, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened
• Index entries for sequences related to Recamán's sequence

Crossrefs

Rows give A063733, A063733, A005132, A066199, A066200.

Programs

Mathematica

T[, 0] = 1; T[n, k_] := T[n, k] = If[t = T[n, k-1] - (n+k-1); t > 0 && FreeQ[Table[T[n, j], {j, 0, k-1}], t], t, T[n, k-1] + (n+k-1)]; Table[ T[n-k, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 18 2018 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 05 2003