A335490 Isosceles triangle read by rows in which each term is the least positive integer satisfying the condition that no row, diagonal, or antidiagonal contains a repeated term.

1, 2, 3, 3, 1, 2, 4, 2, 3, 5, 5, 6, 1, 4, 7, 6, 4, 5, 7, 8, 9, 7, 5, 6, 1, 4, 10, 8, 8, 9, 4, 2, 3, 5, 6, 10, 9, 7, 8, 3, 1, 2, 10, 5, 4, 10, 8, 9, 6, 2, 3, 7, 11, 12, 13, 11, 12, 7, 10, 5, 1, 9, 8, 6, 14, 15, 12, 10, 11, 13, 6, 4, 14, 7, 9, 8, 16, 17, 13, 11

Offset

1,2

Comments

The n-th instance of 1 occurs at index A001844(n-1).

Records occur at 1, 2, 3, 7, 10, 12, 15, 20, 21, 27, 53, 54, 55, 65, ...

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = A296339(n-1) + 1. - Rémy Sigrist, Sep 13 2020

Example

Triangle begins:
       1
      2 3
     3 1 2
    4 2 3 5
   5 6 1 4 7
  6 4 X ...
The value for X is 5 because 1, 2, and 3 are on the diagonal; 4 and 6 are on the antidiagonal; and 4 and 6 are in the row. Therefore 5 is the smallest value that can be inserted so that no diagonal, antidiagonal, or row contains a repeated term.

Crossrefs

Analogs for other tilings: A269526 (square), A334049 (triangular).

Cf. A001844, A274650, A274651, A288530, A288531, A296339.

Sequence in context: A066517 A108132 A106589 * A334290 A294101 A051911

Adjacent sequences: A335487 A335488 A335489 * A335491 A335492 A335493

Keyword

tabl,nonn,more

Author

Alec Jones and Peter Kagey, Sep 12 2020

Status

approved