A244363 Number of toothpicks added at n-th 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).

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

Offset: 1

Author

Omar E. Pol, Jun 26 2014

Keywords

• nonn
• more

Comments

Partial sums give A244362. - Omar E. Pol, Oct 18 2014

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*n-gon described in A237593 to transform it into a pop-up 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 pop-up card has essentially the same structure as the stepped pyramid described in A245092. The holes of the pop-up card are equivalent to the terraces of the stepped pyramid, therefore both objects share many properties. - Omar E. Pol, Mar 08 2023

Crossrefs

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

Formula

a(n) = 2*A244361(n).

a(n) = A244371(n)/4. - Omar E. Pol, Oct 18 2014

a(n) = A274919(n)/2. - Omar E. Pol, Dec 11 2016

Extensions

a(13)-a(28) from Omar E. Pol, Oct 18 2014

Definition clarified by Omar E. Pol, Mar 08 2023

a(29)-a(32) from Omar E. Pol, May 04 2023