A057520 -id:A057520 - cp's OEIS frontend

A085194 Terms of A085193 halved. The repeating part in the first differences of A057520.

1, 3, 1, 2, 9, 1, 3, 1, 2, 5, 1, 2, 4, 29, 1, 3, 1, 2, 9, 1, 3, 1, 2, 5, 1, 2, 4, 13, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 4, 8, 101, 1, 3, 1, 2, 9, 1, 3, 1, 2, 5, 1, 2, 4, 29, 1, 3, 1, 2, 9, 1, 3, 1, 2, 5, 1, 2, 4, 13, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 4, 8, 37, 1, 3, 1, 2, 9, 1, 3, 1, 2, 5, 1, 2, 4, 13, 1, 3, 1, 2

Offset: 0

Antti Karttunen, Jun 14 2003

nonn

A. Karttunen, Table of n, a(n) for n = 0..1429

Partial sums: A085195. Records are given by A079319(n) = A085194(A000108(n+1)-1). Cf. A085189.

a(n) = A085193(n)/2.

A085183 a(n) = A053645(A057520(n)), i.e., the terms of A014486 without their most significant bit (1) and the least significant bit (0).

Original entry on oeis.org

0, 1, 2, 5, 6, 9, 10, 12, 21, 22, 25, 26, 28, 37, 38, 41, 42, 44, 49, 50, 52, 56, 85, 86, 89, 90, 92, 101, 102, 105, 106, 108, 113, 114, 116, 120, 149, 150, 153, 154, 156, 165, 166, 169, 170, 172, 177, 178, 180, 184, 197, 198, 201, 202, 204, 209, 210, 212, 216, 225

Offset: 1

Antti Karttunen, Jun 14 2003

nonn

Same sequence in base 4: A085184.

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

Original entry on oeis.org

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

Mike Stay, Aug 13 2011

nonn

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.

Cf. A000108.

// 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);
}

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]

cp's OEIS Frontend

A085194 Terms of A085193 halved. The repeating part in the first differences of A057520.

Views

Author

Keywords

Links

Crossrefs

Formula

A085183 a(n) = A053645(A057520(n)), i.e., the terms of A014486 without their most significant bit (1) and the least significant bit (0).

Views

Author

Keywords

Crossrefs

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

Views

Author

Keywords

Comments

Crossrefs

Programs

JavaScript

Formula