A395486 Consider the square spiral with its cells numbered starting at 0. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the smallest unoccupied cell not attacked by an existing Red knight, and when it is Red's turn, she places a knight at the smallest unoccupied cell not attacked by an existing Black knight. a(n) = +k if the n-th cell is occupied by the k-th Black knight, a(n) = -k if the n-th cell is occupied by the k-th Red knight, a(n) = 0 otherwise.

1, -1, 2, -2, -3, 3, -4, 0, 0, 4, -5, 5, -6, 0, 0, 6, 0, 0, 0, 0, 7, 8, 0, 0, -7, -8, 0, 0, 0, 0, 9, 10, 0, 0, -9, -10, 11, -11, 0, 0, 12, -12, 13, 0, -13, 0, 0, 14, 15, -14, 16, 0, 0, 0, 0, -15, 17, -16, -17, 0, 0, 18, 0, -18, -19, 19, -20, 20, -21, 21, 22

Offset

0,3

Comments

Each nonzero integer appears exactly once.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

a(A392177(k)) = +k.

a(A392178(k)) = -k.

a(A392179(k)) = 0.

A392180(n) = Sum_{k = 0..n} sign(a(k)).

Example

The first terms alongside the square spiral are:
     0__32___0___0_-30_-29___0__31___0___0_-28
     |                                       |
     0 -19_-18___0__18___0___0_-17_-16__17  30
     |   |                               |   |
     0  19  11_-10__-9___0___0__10___9 -15 -27
     |   |   |                       |   |   |
     0 -20 -11   0___6___0___0__-6   0   0  29
     |   |   |   |               |   |   |   |
     0  20   0   0  -3__-2___2   5   0   0 -26
     |   |   |   |   |       |   |   |   |   |
     0 -21   0   0   3   1__-1  -5   0   0  28
     |   |   |   |   |           |   |   |   |
     0  21  12   0  -4___0___0___4   0   0 -25
     |   |   |   |                   |   |   |
     0  22 -12   7___8___0___0__-7__-8  16  27
     |   |   |                           |   |
     0  23  13___0_-13___0___0__14__15_-14 -24
     |   |                                   |
    33 -22___0___0__24__25___0_-23___0___0__26
     |
    34__35__36___0_-31_-32__37__38___0___0_-33

Prog

(C#) // Use program provided in A392177 with the 3 arguments "- - layout".

Crossrefs

Cf. A392177, A392178, A392179, A392180.

Sequence in context: A093736 A257481 A014589 * A071456 A071505 A071508

Adjacent sequences: A395483 A395484 A395485 * A395487 A395488 A395489

Keyword

sign

Author

Rémy Sigrist, Apr 25 2026

Status

approved