login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) is the total number of edges after n-th stage in the diagram of the symmetries of sigma in which the parts of width > 1 are dissected into subparts of width 1, with a(0) = 0.
3

%I #41 Jul 31 2018 09:57:41

%S 0,4,8,14,20,26,36,42,50,60,70,76,92,98,108,124,136,142,160,166,182,

%T 198,208,214,238,250,260,276,294,300

%N a(n) is the total number of edges after n-th stage in the diagram of the symmetries of sigma in which the parts of width > 1 are dissected into subparts of width 1, with a(0) = 0.

%C All terms are even numbers.

%C Note that in the diagram the number of regions or subparts equals A060831, the partial sums of A001227, n >= 1.

%F a(n) = A317293(n) + A060831(n) - 1 (Euler's formula).

%e Illustration of initial terms (n = 1..9):

%e . _ _ _ _

%e . _ _ _ |_ _ _ |_

%e . _ _ _ |_ _ _| |_ _ _| |_|_

%e . _ _ |_ _ |_ |_ _ |_ _ |_ _ |_ _ |

%e . _ _ |_ _|_ |_ _|_ | |_ _|_ | | |_ _|_ | | |

%e . _ |_ | |_ | | |_ | | | |_ | | | | |_ | | | | |

%e . |_| |_|_| |_|_|_| |_|_|_|_| |_|_|_|_|_| |_|_|_|_|_|_|

%e .

%e . 4 8 14 20 26 36

%e .

%e . _ _ _ _ _

%e . _ _ _ _ _ |_ _ _ _ _|

%e . _ _ _ _ |_ _ _ _ | |_ _ _ _ |_ _

%e . |_ _ _ _| |_ _ _ _| |_ |_ _ _ _| |_ |

%e . |_ _ _ |_ |_ _ _ |_ |_ _ |_ _ _ |_ |_|_ _

%e . |_ _ _| |_|_ _ |_ _ _| |_|_ _ | |_ _ _| |_|_ _ | |

%e . |_ _ |_ _ | | |_ _ |_ _ | | | |_ _ |_ _ | | | |

%e . |_ _|_ | | | | |_ _|_ | | | | | |_ _|_ | | | | | |

%e . |_ | | | | | | |_ | | | | | | | |_ | | | | | | | |

%e . |_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|

%e .

%e . 42 50 60

%e .

%e .

%e Illustration of the two-dimensional diagram after 29 stages (contains 300 edges, 239 vertices and 62 regions or subparts):

%e ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _

%e |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

%e |_ _ _ _ _ _ _ _ _ _ _ _ _ _ |

%e |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |

%e |_ _ _ _ _ _ _ _ _ _ _ _ _ | |

%e |_ _ _ _ _ _ _ _ _ _ _ _ _| | |

%e |_ _ _ _ _ _ _ _ _ _ _ _ | | |_ _ _

%e |_ _ _ _ _ _ _ _ _ _ _ _| | |_ _ _ |

%e |_ _ _ _ _ _ _ _ _ _ _ | | |_ _ | |_

%e |_ _ _ _ _ _ _ _ _ _ _| | |_ _ _| |_ |_

%e |_ _ _ _ _ _ _ _ _ _ | | |_ _ |_ _| |_|_

%e |_ _ _ _ _ _ _ _ _ _| | |_ _ | |_ |_ _ |_ _

%e |_ _ _ _ _ _ _ _ _ | |_ _ _| |_ |_ | |_ _ |

%e |_ _ _ _ _ _ _ _ _| | |_ _ |_ |_ |_|_ _ | |

%e |_ _ _ _ _ _ _ _ | |_ _ |_ _|_ |_ _ | | | |_ _ _ _ _ _

%e |_ _ _ _ _ _ _ _| | |_ _| |_ | |_ _ | | |_|_ _ _ _ _ | |

%e |_ _ _ _ _ _ _ | |_ _ |_ |_|_ | | |_|_ _ _ _ _ | | | |

%e |_ _ _ _ _ _ _| |_ _ |_ |_ _ | | |_ _ _ _ _ | | | | | |

%e |_ _ _ _ _ _ | |_ |_ |_ | | |_|_ _ _ _ | | | | | | | |

%e |_ _ _ _ _ _| |_ _| |_|_ | |_|_ _ _ _ | | | | | | | | | |

%e |_ _ _ _ _ | |_ |_ _ | |_ _ _ _ | | | | | | | | | | | |

%e |_ _ _ _ _| |_ |_ | |_|_ _ _ | | | | | | | | | | | | | |

%e |_ _ _ _ |_ _|_ |_|_ _ _ | | | | | | | | | | | | | | | |

%e |_ _ _ _| |_ | |_ _ _ | | | | | | | | | | | | | | | | | |

%e |_ _ _ |_ |_|_ _ | | | | | | | | | | | | | | | | | | | |

%e |_ _ _| |_|_ _ | | | | | | | | | | | | | | | | | | | | | |

%e |_ _ |_ _ | | | | | | | | | | | | | | | | | | | | | | | |

%e |_ _|_ | | | | | | | | | | | | | | | | | | | | | | | | | |

%e |_ | | | | | | | | | | | | | | | | | | | | | | | | | | | |

%e |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|

%e .

%Y For the definition of "subparts" see A279387.

%Y For the triangle of sums of subparts see A279388.

%Y Cf. A317293 (number of vertices).

%Y Cf. A060831 (number of regions or subparts).

%Y Compare with A317109 (analog for the diagram that contains only parts).

%Y First differs from A317109 at a(6).

%Y Cf. A000203, A001227, A196020, A235791, A237048, A237590, A237591, A237270, A237271, A237593, A245092, A244050, A262626, A280850, A280851, A280940, A285901, A294723, A296508.

%K nonn,more

%O 0,2

%A _Omar E. Pol_, Jul 27 2018