A368148 Square array A(n, k), n, k > 0, read and filled in the greedy way by upwards antidiagonals such that A(n, k) corresponds to the size of the connected component (relative to the Von Neumann neighborhood) of terms equal to A(n, k) including the position (n, k).

1, 2, 2, 2, 1, 2, 1, 3, 3, 1, 2, 2, 3, 2, 2, 2, 1, 2, 2, 1, 2, 1, 3, 3, 1, 3, 3, 1, 2, 2, 3, 2, 2, 3, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1

Offset

1,2

Comments

The array is doubly periodic (see first formula) and consists of the following repeating 3 X 3 pattern with two components of 1 1's, two components of 2 2's and one component of 3 3's:

+---+-------+

| 1 | 2 2 |

+---+---+---+

| 2 | 1 | 3 |

| +---+ |

| 2 | 3 3 |

+---+-------+

Links

Table of n, a(n) for n=1..91.

Formula

A(n+3, k) = A(n, k+3) = A(n, k).

A(n, k) = A(k, n).

Example

Array A(n, k) begins:
  n\k | 1  2  3  4  5  6  7  8  9 10
  ----+-----------------------------
    1 | 1  2  2  1  2  2  1  2  2  1
    2 | 2  1  3  2  1  3  2  1  3  2
    3 | 2  3  3  2  3  3  2  3  3  2
    4 | 1  2  2  1  2  2  1  2  2  1
    5 | 2  1  3  2  1  3  2  1  3  2
    6 | 2  3  3  2  3  3  2  3  3  2
    7 | 1  2  2  1  2  2  1  2  2  1
    8 | 2  1  3  2  1  3  2  1  3  2
    9 | 2  3  3  2  3  3  2  3  3  2
   10 | 1  2  2  1  2  2  1  2  2  1
.
We can chose A(1, 1) = 1.
A(2, 1) cannot equal 1; we chose A(2, 1) = 2.
Likewise we chose A(1, 2).
A(2, 2) cannot equal 2 as this would imply a component with 3 or more 2's.
So, by necessity, we chose A(3, 1) = A(1, 3) = 2.
We chose A(2, 2) = 1.
We chose A(4, 1) = 1.
A(3, 2) cannot equal 1 or 2; we chose A(3, 2) = 3.
Likewise we chose A(2, 3) = 3.
We chose A(1, 4) = 1.
A(5, 1) cannot equal 1; we chose A(5, 1) = 2.
A(4, 2) cannot equal 1 (or 3); we chose A(4, 2) = 2.
By necessity, A(3, 3) = 3.
etc.

Prog

(PARI) A(n, k) = { [1, 2, 2; 2, 1, 3; 2, 3, 3][1+(n-1)%3, 1+(k-1)%3] }

Crossrefs

Cf. A130196 (one-dimensional variant).

Sequence in context: A237523 A339812 A238568 * A238421 A105154 A076447

Adjacent sequences: A368145 A368146 A368147 * A368149 A368150 A368151

Keyword

nonn,tabl,easy

Author

Rémy Sigrist, Dec 13 2023

Status

approved