OFFSET

0,3

COMMENTS

To find the number to enter in a cell (assuming the sector is oriented as in the illustration in the link), look at all the numbers in the cells directly above the cell, in the cells to the "North-West", and in the cells to the "South-West", and take their "mex" (the smallest missing number).

The 0-cells in the array all lie on a perfectly straight line (in contrast to the situation in A274528). Also a(n) = 0 iff n = 2*m*(m+1) for some m.

LINKS

Rémy Sigrist, Rows n = 0..200, flattened

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Rémy Sigrist, PARI program for A296339

N. J. A. Sloane, Illustration of initial rows of the sector.

EXAMPLE

The initial rows are as follows (however, this does not show the adjancies between the cells correctly - for that, see the illustration in the link):

0;

1, 2;

2, 0, 1;

3, 1, 2, 4;

4, 5, 0, 3, 6;

5, 3, 4, 6, 7, 8;

6, 4, 5, 0, 3, 9, 7;

7, 8, 3, 1, 2, 4, 5, 9;

8, 6, 7, 2, 0, 1, 9, 4, 3;

9, 7, 8, 5, 1, 2, 6, 10, 11, 12;

10, 11, 6, 9, 4, 0, ...

...

For example, referring to the illustration in the link and NOT to the triangle here, consider the first 5 in the array. The reason this is 5 is because in the column of cells above that cell we can see 2,0,1, to the NW we see 3, and to the SW we see 4, and the smallest missing number is 5.

MATHEMATICA

ab = Table[0, {13}];

nw = ab;

A296339 = Reap[For[s = 1, s <= Length[ab], s++, sw = 0; For[c = 1, c <= s, c++, x = BitOr[ab[[c]], BitOr[nw[[s-c+1]], sw]]; v = IntegerExponent[x+1, 2]; Sow[v]; p = 2^v; sw += p; ab[[c]] += p; nw[[s-c+1]] += p]]][[2, 1]] (* Jean-François Alcover, Dec 18 2017, after Rémy Sigrist *) (* I changed the first line, which was ab = Table[0, 13]; , to make this compatible with older versions of MMA - N. J. A. Sloane, Feb 03 2018 *)

PROG

(PARI) See Links section.

CROSSREFS

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Dec 10 2017

EXTENSIONS

More terms from Rémy Sigrist, Dec 11 2017

STATUS

approved