A274919 Sum of all perimeters of all parts of the symmetric representation of sigma(n).

4, 8, 12, 16, 16, 24, 20, 32, 32, 40, 28, 48, 32, 52, 52, 64, 40, 72, 44, 80, 72, 76, 52, 96, 68, 88, 88, 112, 64, 120, 68, 128

Offset

1,1

Comments

a(n) is also the number of toothpicks added at n-th stage in the toothpick structure of the symmetric representation of sigma in two quadrants (without the axis x and y).

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = 4*A244361(n) = 2*A244363(n) = A244371(n)/2.

a(n) = A008586(n) - 2*A279228(n). - Omar E. Pol, May 04 2023

Example

Illustration of a(9) = 32:
.         12
.     _ _ _ _ _
.    |_ _ _ _ _|
.               _ _ 8
.              |_  |
.                |_|  _
.                    | |
.                    | |
.                    | |  12
.                    | |
.                    |_|
.
For n = 9 the symmetric representation of sigma(9) = 13 has three parts of areas 5, 3, 5 respectively. The perímeters of the parts are 12, 8 and 12 as shown above. The sum of the perimeters is 12 + 8 + 12 = 32, so a(9) = 32.

Crossrefs

Cf. A000203, A008586, A196020, A236104, A237270, A237271, A237593, A244361, A244363, A244370, A244371, A245092, A262626, A279228.

Sequence in context: A081747 A331061 A020647 * A196032 A130702 A355740

Adjacent sequences: A274916 A274917 A274918 * A274920 A274921 A274922

Keyword

nonn,more

Author

Omar E. Pol, Dec 11 2016

Extensions

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

Status

approved