A194045 Numbers whose binary expansion is a preorder traversal of a binary tree

0, 4, 20, 24, 84, 88, 100, 104, 112, 340, 344, 356, 360, 368, 404, 408, 420, 424, 432, 452, 456, 464, 480, 1364, 1368, 1380, 1384, 1392, 1428, 1432, 1444, 1448, 1456, 1476, 1480, 1488, 1504, 1620, 1624, 1636, 1640, 1648, 1684, 1688, 1700, 1704, 1712, 1732, 1736, 1744, 1760, 1812, 1816, 1828, 1832, 1840, 1860, 1864, 1872, 1888, 1924, 1928, 1936, 1952, 1984

Offset

0,2

Comments

When traversing the tree in preorder, emit 1 at each node and 0 if it has no child on the current branch. The smallest binary tree is empty, so we emit 0 at the root; thus a(0) = 0. The next binary tree is a single node (emit 1) with no left (emit 0) or right child (emit 0); thus a(1) = 100 in binary or 4.

Links

Table of n, a(n) for n=0..64.

Formula

a(n) = 4 * A057520(n). [Joerg Arndt, Sep 22 2012]

a(0)=0, a(n) = 2 * A014486(n) for n>=1. [Joerg Arndt, Sep 22 2012]

Prog

(JavaScript)
// n is the number of internal nodes (or 1s in the binary expansion)
// f is a function to display each result
function trees(n, f) {
  // h is the "height", thinking of 1 as a step up and 0 as a step down
  // s is the current state
  function enumerate(n, h, s, f) {
    if (n===0 && h===0) { f(2 * s); }
    else {
      if (h > 0) { enumerate(n, h - 1, 2 * s, f) }
      if (n > 0) { enumerate(n - 1, h + 1, 2 * s + 1, f) }
    }
  }
  enumerate(n, 0, 0, f);
}

Crossrefs

Cf. A000108.

Sequence in context: A298040 A174134 A032425 * A097251 A202070 A198831

Adjacent sequences: A194042 A194043 A194044 * A194046 A194047 A194048

Keyword

nonn

Author

Mike Stay, Aug 13 2011

Status

approved