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 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 FORMULA a(n) = 4*A244362(n) = 8*A244360(n). EXAMPLE Illustration of the structure after 16 stages (Contains 960 toothpicks): . .                 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .                |  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  | .                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | .             _ _| |  _ _ _ _ _ _ _ _ _ _ _ _ _ _  | |_ _ .           _|  _ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _  |_ .         _|  _|  _| |  _ _ _ _ _ _ _ _ _ _ _ _  | |_  |_  |_ .        |  _|   |_ _| |_ _ _ _ _ _ _ _ _ _ _ _| |_ _|   |_  | .   _ _ _| |  _ _|     |  _ _ _ _ _ _ _ _ _ _  |     |_ _  | |_ _ _ .  |  _ _ _|_| |      _| |_ _ _ _ _ _ _ _ _ _| |_      | |_|_ _ _  | .  | | |  _ _ _|    _|_ _|  _ _ _ _ _ _ _ _  |_ _|_    |_ _ _  | | | .  | | | | |  _ _ _| |  _| |_ _ _ _ _ _ _ _| |_  | |_ _ _  | | | | | .  | | | | | | |  _ _|_|  _|  _ _ _ _ _ _  |_  |_|_ _  | | | | | | | .  | | | | | | | | |  _ _|   |_ _ _ _ _ _|   |_ _  | | | | | | | | | .  | | | | | | | | | | |  _ _|  _ _ _ _  |_ _  | | | | | | | | | | | .  | | | | | | | | | | | | |  _|_ _ _ _|_  | | | | | | | | | | | | | .  | | | | | | | | | | | | | | |  _ _  | | | | | | | | | | | | | | | .  | | | | | | | | | | | | | | | |   | | | | | | | | | | | | | | | | .  | | | | | | | | | | | | | | | |_ _| | | | | | | | | | | | | | | | .  | | | | | | | | | | | | | |_|_ _ _ _|_| | | | | | | | | | | | | | .  | | | | | | | | | | | |_|_  |_ _ _ _|  _|_| | | | | | | | | | | | .  | | | | | | | | | |_|_    |_ _ _ _ _ _|    _|_| | | | | | | | | | .  | | | | | | | |_|_ _  |_  |_ _ _ _ _ _|  _|  _ _|_| | | | | | | | .  | | | | | |_|_ _  | |_  |_ _ _ _ _ _ _ _|  _| |  _ _|_| | | | | | .  | | | |_|_ _    |_|_ _| |_ _ _ _ _ _ _ _| |_ _|_|    _ _|_| | | | .  | |_|_ _ _  |     |_  |_ _ _ _ _ _ _ _ _ _|  _|     |  _ _ _|_| | .  |_ _ _  | |_|_      | |_ _ _ _ _ _ _ _ _ _| |      _|_| |  _ _ _| .        | |_    |_ _  |_ _ _ _ _ _ _ _ _ _ _ _|  _ _|    _| | .        |_  |_  |_  | |_ _ _ _ _ _ _ _ _ _ _ _| |  _|  _|  _| .          |_  |_ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _|  _| .            |_ _  | |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |  _ _| .                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | .                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | .                |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| . 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 January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)