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.

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, 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, 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

Offset: 1

Author

Michel Marcus, Jan 26 2014

Keywords

• nonn
• tabl

Comments

First column is A051162. Right diagonal is all zeros.

Examples

			Triangle where distances are measured begins:
1
2 3
4 5 6
7 8 9 10
Distance between 1 and 1 is 0, hence T(1, 1) = 0.
Distance between 2 and 1 is 1, and between 2 and 2 is 0. Hence second row of this triangle is 1, 0.
Triangle starts:
0;
1, 0;
2, 1, 0;
2, 1, 2, 0;
3, 2, 1, 1, 0;
		

Crossrefs

Cf. A236345.

Programs

PARI

getxy(n) = {y = sqrtint(2*n); if (n<=y*(y+1)/2, y--); x = n - y*(y+1)/2; [x, y];}
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(););}