

A236459


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


0



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
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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



