A111796 - OEIS

%I #6 Nov 23 2013 23:44:50

%S 1,2,3,4,5,7,8,9,16,6,11,13,17,19,23,25,27,32,49,53,64,81,128,256,512,

%T 65536,10,12,14,18

%N Positive integers sorted by rote weight (A062537) and omega (A001221).

%C Positive integers m sorted by g(m) = A062537(m) and w(m) = A001221(m).

%C Defining the "wayage" of a rooted tree to be its root degree, the rote corresponding to the positive integer m has a wayage of w(m) = omega(m) = A001221(m).

%H J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>

%e Table of Integers, Primal Codes, Sort Parameters and Subtotals

%e ` ` a ` code` ` | g w | s | t

%e ----------------+-----+---+---

%e ` ` 1 = { } ` ` | 0 0 | 1 | 1

%e ----------------+-----+---+---

%e ` ` 2 = 1:1 ` ` | 1 1 | 1 | 1

%e ----------------+-----+---+---

%e ` ` 3 = 2:1 ` ` | 2 1 | ` |

%e ` ` 4 = 1:2 ` ` | 2 1 | 2 | 2

%e ----------------+-----+---+---

%e ` ` 5 = 3:1 ` ` | 3 1 | ` |

%e ` ` 7 = 4:1 ` ` | 3 1 | ` |

%e ` ` 8 = 1:3 ` ` | 3 1 | ` |

%e ` ` 9 = 2:2 ` ` | 3 1 | ` |

%e ` `16 = 1:4 ` ` | 3 1 | 5 |

%e ----------------+-----+---+---

%e ` ` 6 = 1:1 2:1 | 3 2 | 1 | 6

%e ----------------+-----+---+---

%e ` `11 = 5:1 ` ` | 4 1 | ` |

%e ` `13 = 6:1 ` ` | 4 1 | ` |

%e ` `17 = 7:1 ` ` | 4 1 | ` |

%e ` `19 = 8:1 ` ` | 4 1 | ` |

%e ` `23 = 9:1 ` ` | 4 1 | ` |

%e ` `25 = 3:2 ` ` | 4 1 | ` |

%e ` `27 = 2:3 ` ` | 4 1 | ` |

%e ` `32 = 1:5 ` ` | 4 1 | ` |

%e ` `49 = 4:2 ` ` | 4 1 | ` |

%e ` `53 = 16:1` ` | 4 1 | ` |

%e ` `64 = 1:6 ` ` | 4 1 | ` |

%e ` `81 = 2:4 ` ` | 4 1 | ` |

%e ` 128 = 1:7 ` ` | 4 1 | ` |

%e ` 256 = 1:8 ` ` | 4 1 | ` |

%e ` 512 = 1:9 ` ` | 4 1 | ` |

%e 65536 = 1:16` ` | 4 1 |16 |

%e ----------------+-----+---+---

%e ` `10 = 1:1 3:1 | 4 2 | ` |

%e ` `12 = 1:2 2:1 | 4 2 | ` |

%e ` `14 = 1:1 4:1 | 4 2 | ` |

%e ` `18 = 1:1 2:2 | 4 2 | 4 |20

%e ----------------+-----+---+---

%e a = this sequence

%e g = rote weight in gammas = A062537

%e w = rote wayage in gammas = A001221

%e s = count in (g, w) class = A111797

%e t = count in weight class = A061396

%Y Cf. A001221, A061396, A062504, A062537, A062860.

%Y Cf. A111797, A111798, A111800.

%K nonn,tabf

%O 1,2

%A _Jon Awbrey_, Sep 01 2005