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

1,4

Comments

First column is A051162. Right diagonal is all zeros.

Links

Table of n, a(n) for n=1..105.

Example

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;

Prog

(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(); ); }

Crossrefs

Cf. A236345.

Sequence in context: A330374 A207869 A130210 * A190427 A287108 A333948

Adjacent sequences: A236456 A236457 A236458 * A236460 A236461 A236462

Keyword

nonn,tabl

Author

Michel Marcus, Jan 26 2014

Status

approved