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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. 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS First column is A051162. Right diagonal is all zeros. LINKS 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

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)