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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).
2
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))
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
KEYWORD
nonn,tabl
AUTHOR
Aidan Clarke, Sep 22 2020
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Sep 24 2020
STATUS
approved