

A244363


Number of toothpicks added at nth stage in the toothpick structure of the symmetric representation of sigma of the first n positive integers in the first quadrant (without the axis x and y).


12



2, 4, 6, 8, 8, 12, 10, 16, 16, 20, 14, 24, 16, 26, 26, 32, 20, 36, 22, 40, 36, 38, 26, 48, 34, 44, 44, 56, 32, 60, 34, 64
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OFFSET

1,1


COMMENTS

a(n) is also the sum of semiperimeters of the parts of the symmetric representation of sigma(n).  Omar E. Pol, Dec 11 2016
It appears that a(n) is also the total length of the horizontal cuts that must be made at level n, starting from the top, in the diagram of the "isosceles triangle shaped" 4*ngon described in A237593 to transform it into a popup card which when folded 90 degrees has the property that the total area of its holes at level n is equal to A000203(n). Note that the popup card has essentially the same structure as the stepped pyramid described in A245092. The holes of the popup card are equivalent to the terraces of the stepped pyramid, therefore both objects share many properties.  Omar E. Pol, Mar 08 2023


LINKS



FORMULA



CROSSREFS

Cf. A000203, A196020, A237270, A237271, A237593, A244360, A244361, A244362, A244370, A244371, A245092, A262626, A274919.


KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



