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A244370 Total number of toothpicks after n-th stage in the toothpick structure of the symmetric representation of sigma in the four quadrants. 9
8, 24, 48, 80, 112, 160, 200, 264, 328, 408, 464, 560, 624, 728, 832, 960, 1040, 1184, 1272, 1432, 1576, 1728, 1832, 2024, 2160, 2336, 2512, 2736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Partial sums of A244371.

If we use toothpicks of length 1/2, so the area of the central square is equal to 1. The total area of the structure after n-th stage is equal to A024916(n), the sum of all divisors of all positive integers <= n, hence the total area of the n-th set of symmetric regions added at n-th stage is equal to sigma(n) = A000203(n), the sum of divisors of n.

If we use toothpicks of length 1, so the number of cells (and the area) of the central square is equal to 4. The number of cells (and the total area) of the structure after n-th stage is equal to 4*A024916(n) = A243980(n), hence the number of cells (and the total area) of the n-th set of symmetric regions added at n-th stage is equal to 4*A000203(n) = A239050(n).

LINKS

Table of n, a(n) for n=1..28.

FORMULA

a(n) = 4*A244362(n) = 8*A244360(n).

EXAMPLE

Illustration of the structure after 16 stages (Contains 960 toothpicks):

.

.                 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

.                |  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  |

.                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |

.             _ _| |  _ _ _ _ _ _ _ _ _ _ _ _ _ _  | |_ _

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.  | | | | | | | | | | |  _ _|  _ _ _ _  |_ _  | | | | | | | | | | |

.  | | | | | | | | | | | | |  _|_ _ _ _|_  | | | | | | | | | | | | |

.  | | | | | | | | | | | | | | |  _ _  | | | | | | | | | | | | | | |

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.  | | | | | | | | | | | | | | | |_ _| | | | | | | | | | | | | | | |

.  | | | | | | | | | | | | | |_|_ _ _ _|_| | | | | | | | | | | | | |

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.  | | | | | | | |_|_ _  |_  |_ _ _ _ _ _|  _|  _ _|_| | | | | | | |

.  | | | | | |_|_ _  | |_  |_ _ _ _ _ _ _ _|  _| |  _ _|_| | | | | |

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.  | |_|_ _ _  |     |_  |_ _ _ _ _ _ _ _ _ _|  _|     |  _ _ _|_| |

.  |_ _ _  | |_|_      | |_ _ _ _ _ _ _ _ _ _| |      _|_| |  _ _ _|

.        | |_    |_ _  |_ _ _ _ _ _ _ _ _ _ _ _|  _ _|    _| |

.        |_  |_  |_  | |_ _ _ _ _ _ _ _ _ _ _ _| |  _|  _|  _|

.          |_  |_ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _|  _|

.            |_ _  | |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |  _ _|

.                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |

.                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |

.                |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

.

CROSSREFS

Cf. A000203, A004125, A024916, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239050, A239660, A239931-A239934, A243980, A244050, A244360-A244363, A244371, A244970, A244971, A245092.

Sequence in context: A306415 A122812 A022763 * A179682 A033996 A333714

Adjacent sequences:  A244367 A244368 A244369 * A244371 A244372 A244373

KEYWORD

nonn,more

AUTHOR

Omar E. Pol, Jun 26 2014

EXTENSIONS

a(8) corrected and more terms from Omar E. Pol, Oct 18 2014

STATUS

approved

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Last modified September 18 22:56 EDT 2020. Contains 337174 sequences. (Running on oeis4.)