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 A257571 Triangular array read by rows: d(h,k) = distance between h and k in the tree at A232558, for h >=0, k = 0..h. 3
 0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 2, 0, 4, 3, 2, 3, 1, 0, 4, 3, 2, 1, 3, 4, 0, 5, 4, 3, 2, 4, 5, 1, 0, 4, 3, 2, 3, 1, 2, 4, 5, 0, 5, 4, 3, 4, 2, 3, 5, 6, 1, 0, 5, 4, 3, 4, 2, 1, 5, 6, 3, 4, 0, 6, 5, 4, 5, 3, 2, 6, 7, 4, 5, 1, 0, 5, 4, 3, 2, 4, 5, 1, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The distance between h and k is the length of the path from h to k in the tree defined from the root 0 by edges from x to x+1 and x to 2x if x is even, and an edge from x to x+1 if x is odd.  This is the tree defined at A232558; it is a subtree of the tree defined at A257569. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE First ten rows: 0 1  0 2  1  0 3  2  1  0 3  2  1  2  0 4  3  2  3  1  0 4  3  2  1  3  4  0 5  4  3  2  4  5  1  0 4  3  2  3  1  2  4  5  0 5  4  3  5  2  3  6  7  1  0 d(6,4) = 3 counts the edges in the path 6,3,2,4; d(46,21) = 6 counts the edges in the path 46,23,22,11,10,20,21. MATHEMATICA f[{x_, y_}] := f[x, y] = If[EvenQ[x], {y, x/2}, {x - 1, y}]; g[{x_, y_}] := g[x, y] = Drop[FixedPointList[f, {x, y}], -1]; s[n_] := s[n] = Reverse[Select[Sort[Flatten[Select[g[{n, 0}], #[] == 0 &]]], # > 0 &]]; m[h_, k_] := m[h, k] = Max[Intersection[s[h], s[k]]]; j[h_, k_] := j[h, k] = Join[Select[s[h], # >= m[h, k] &], Reverse[Select[s[k], # > m[h, k] &]]]; d[h_, k_] := d[h, k] = If[k*h == 0, Length[j[h, k]], -1 + Length[j[h, k]]]; TableForm[Table[d[h, k], {h, 0, 59}, {k, 0, 59}]];  (* A257570 array *) Flatten[Table[d[h - k, k], {h, 0, 59}, {k, 0, h}]]; (* A257570 sequence *) CROSSREFS Cf. A257570, A232558. Sequence in context: A074984 A112658 A190693 * A219649 A292160 A025581 Adjacent sequences:  A257568 A257569 A257570 * A257572 A257573 A257574 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, May 01 2015 STATUS approved

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Last modified February 27 03:50 EST 2020. Contains 332299 sequences. (Running on oeis4.)