cp's OEIS Frontend

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

%I A194045 #13 Jul 22 2025 12:32:11
%S A194045 0,4,20,24,84,88,100,104,112,340,344,356,360,368,404,408,420,424,432,
%T A194045 452,456,464,480,1364,1368,1380,1384,1392,1428,1432,1444,1448,1456,
%U A194045 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 A194045 Numbers whose binary expansion is a preorder traversal of a binary tree.
%C A194045 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 A194045 a(n) = 4 * A057520(n). [_Joerg Arndt_, Sep 22 2012]
%F A194045 a(0)=0, a(n) = 2 * A014486(n) for n>=1. [_Joerg Arndt_, Sep 22 2012]
%o A194045 (JavaScript)
%o A194045 // n is the number of internal nodes (or 1s in the binary expansion)
%o A194045 // f is a function to display each result
%o A194045 function trees(n, f) {
%o A194045   // h is the "height", thinking of 1 as a step up and 0 as a step down
%o A194045   // s is the current state
%o A194045   function enumerate(n, h, s, f) {
%o A194045     if (n===0 && h===0) { f(2 * s); }
%o A194045     else {
%o A194045       if (h > 0) { enumerate(n, h - 1, 2 * s, f) }
%o A194045       if (n > 0) { enumerate(n - 1, h + 1, 2 * s + 1, f) }
%o A194045     }
%o A194045   }
%o A194045   enumerate(n, 0, 0, f);
%o A194045 }
%Y A194045 Cf. A000108.
%K A194045 nonn
%O A194045 0,2
%A A194045 _Mike Stay_, Aug 13 2011