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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).

%I A337804 #33 Oct 23 2020 12:24:17
%S A337804 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,
%T A337804 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,
%U A337804 26,27,28,29,7,16,1,4,2,19,30,31,32,33,34,35,30,2,12,11
%N 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).
%C A337804 Each value is determined by placing the least possible nonnegative integer that will abide by the rules of the sequence.
%H A337804 Rémy Sigrist, <a href="/A337804/b337804.txt">Table of n, a(n) for n = 1..10011</a> (rows for n = 1..141, flattened)
%H A337804 Rémy Sigrist, <a href="/A337804/a337804.png">Colored representation of the first 500 rows</a> (where the hue is function of T(n,k))
%H A337804 Rémy Sigrist, <a href="/A337804/a337804_1.png">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)</a> (where the hue is function of T(n, k))
%H A337804 Rémy Sigrist, <a href="/A337804/a337804.gp.txt">PARI program for A337804</a>
%e A337804 Triangle begins:
%e A337804 0;
%e A337804 0, 0;
%e A337804 1, 2, 1;
%e A337804 0, 3, 4, 0;
%e A337804 3, 5, 2, 6, 3;
%e A337804 2, 7, 8, 5, 1, 9;
%e A337804 ...
%o A337804 (PARI)
%o A337804 T(n)={my(v=vector(n), S=Set(), L=List());
%o A337804   for(n=1, #v, v[n]=vector(n); for(k=1, n, my(i=1);
%o A337804     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++);
%o A337804     if(i>#L, listput(L, []));
%o A337804     L[i] = concat(L[i], [[n,k]]);
%o A337804     v[n][k] = i-1 )); v
%o A337804 }
%o A337804 concat(T(12)) \\ _Andrew Howroyd_, Sep 24 2020
%o A337804 (PARI) See Links section.
%Y A337804 Cf. A337226 (linear version).
%K A337804 nonn,tabl
%O A337804 1,5
%A A337804 _Aidan Clarke_, Sep 22 2020
%E A337804 Terms a(46) and beyond from _Andrew Howroyd_, Sep 24 2020