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A236459 Regular triangle: T(n, k) Manhattan distance between n and k in a left-aligned triangle with next M natural numbers in row M.

%I A236459 #11 Dec 09 2014 03:32:59
%S A236459 0,1,0,2,1,0,2,1,2,0,3,2,1,1,0,4,3,2,2,1,0,3,2,3,1,2,3,0,4,3,2,2,1,2,
%T A236459 1,0,5,4,3,3,2,1,2,1,0,6,5,4,4,3,2,3,2,1,0,4,3,4,2,3,4,1,2,3,4,0,5,4,
%U A236459 3,3,2,3,2,1,2,3,1,0,6,5,4,4,3,2,3,2,1,2,2,1,0,7,6,5,5,4,3,4,3,2,1,3,2,1,0
%N A236459 Regular triangle: T(n, k) Manhattan distance between n and k in a left-aligned triangle with next M natural numbers in row M.
%C A236459 First column is A051162. Right diagonal is all zeros.
%e A236459 Triangle where distances are measured begins:
%e A236459 1
%e A236459 2 3
%e A236459 4 5 6
%e A236459 7 8 9 10
%e A236459 Distance between 1 and 1 is 0, hence T(1, 1) = 0.
%e A236459 Distance between 2 and 1 is 1, and between 2 and 2 is 0. Hence second row of this triangle is 1, 0.
%e A236459 Triangle starts:
%e A236459 0;
%e A236459 1, 0;
%e A236459 2, 1, 0;
%e A236459 2, 1, 2, 0;
%e A236459 3, 2, 1, 1, 0;
%o A236459 (PARI) getxy(n) = {y = sqrtint(2*n); if (n<=y*(y+1)/2, y--); x = n - y*(y+1)/2; [x, y];}
%o A236459 trg(nn) = {i= 1; for (n = 1, nn, v = getxy(n); for (k = 1, n, nv = getxy(k); print1(abs(nv[1]-v[1])+abs(nv[2]-v[2]), ", ");); print(););}
%Y A236459 Cf. A236345.
%K A236459 nonn,tabl
%O A236459 1,4
%A A236459 _Michel Marcus_, Jan 26 2014