A337804 Lexicographically earliest triangle of nonnegative integers read by rows such that for each pair (x,y) != (0,0), there is at most one pair (n,k) such that T(n,k) = T(n+x,k+y).

0, 0, 0, 1, 2, 1, 0, 3, 4, 0, 3, 5, 2, 6, 3, 2, 7, 8, 5, 1, 9, 1, 0, 9, 10, 11, 7, 2, 6, 4, 12, 13, 14, 15, 0, 8, 9, 11, 16, 17, 18, 19, 20, 6, 5, 5, 15, 21, 22, 23, 24, 25, 21, 3, 10, 8, 1, 3, 26, 27, 28, 29, 7, 16, 1, 4, 2, 19, 30, 31, 32, 33, 34, 35, 30, 2, 12, 11

Offset: 1

Author

Aidan Clarke, Sep 22 2020

Keywords

• nonn
• tabl

Comments

Each value is determined by placing the least possible nonnegative integer that will abide by the rules of the sequence.

Examples

			Triangle begins:
0;
0, 0;
1, 2, 1;
0, 3, 4, 0;
3, 5, 2, 6, 3;
2, 7, 8, 5, 1, 9;
...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141, flattened)
• Rémy Sigrist, Colored representation of the first 500 rows (where the hue is function of T(n,k))
• Rémy Sigrist, Colored scatterplot of (x, y) such that T(n, k) = T(n+x, k+y) and max(n, n+x) <= 500 and (x, y) <> (0, 0) (where the hue is function of T(n, k))
• Rémy Sigrist, PARI program for A337804

Crossrefs

Cf. A337226 (linear version).

Programs

PARI

T(n)={my(v=vector(n), S=Set(), L=List());
  for(n=1, #v, v[n]=vector(n); for(k=1, n, my(i=1);
    while(i<=#L, my(P=Set([[n-p[1], k-p[2]] | p<-L[i]])); if(!#setintersect(P,S), S = setunion(S,P); break); i++);
    if(i>#L, listput(L, []));
    L[i] = concat(L[i], [[n,k]]);
    v[n][k] = i-1 )); v
}
concat(T(12)) \\ Andrew Howroyd, Sep 24 2020

PARI

See Links section.

Extensions

Terms a(46) and beyond from Andrew Howroyd, Sep 24 2020