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%I #11 Jun 23 2022 20:30:15
%S 0,4,20,24,84,88,100,104,112,340,344,356,360,368,404,408,420,424,432,
%T 452,456,464,480,1364,1368,1380,1384,1392,1428,1432,1444,1448,1456,
%U 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
%N Numbers whose binary expansion is a preorder traversal of a binary tree
%C 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.
%F a(n) = 4 * A057520(n). [_Joerg Arndt_, Sep 22 2012]
%F a(0)=0, a(n) = 2 * A014486(n) for n>=1. [_Joerg Arndt_, Sep 22 2012]
%o (JavaScript)
%o // n is the number of internal nodes (or 1s in the binary expansion)
%o // f is a function to display each result
%o function trees(n, f) {
%o // h is the "height", thinking of 1 as a step up and 0 as a step down
%o // s is the current state
%o function enumerate(n, h, s, f) {
%o if (n===0 && h===0) { f(2 * s); }
%o else {
%o if (h > 0) { enumerate(n, h - 1, 2 * s, f) }
%o if (n > 0) { enumerate(n - 1, h + 1, 2 * s + 1, f) }
%o }
%o }
%o enumerate(n, 0, 0, f);
%o }
%Y Cf. A000108.
%K nonn
%O 0,2
%A _Mike Stay_, Aug 13 2011
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