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

1,5

Comments

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

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

Example

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

Prog

(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.

Crossrefs

Cf. A337226 (linear version).

Sequence in context: A154557 A049242 A108887 * A357368 A193401 A220399

Adjacent sequences: A337801 A337802 A337803 * A337805 A337806 A337807

Keyword

nonn,tabl

Author

Aidan Clarke, Sep 22 2020

Extensions

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

Status

approved