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%I #31 May 04 2023 10:54:06
%S 4,8,12,16,16,24,20,32,32,40,28,48,32,52,52,64,40,72,44,80,72,76,52,
%T 96,68,88,88,112,64,120,68,128
%N Sum of all perimeters of all parts of the symmetric representation of sigma(n).
%C 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).
%F a(n) = 4*A244361(n) = 2*A244363(n) = A244371(n)/2.
%F a(n) = A008586(n) - 2*A279228(n). - _Omar E. Pol_, May 04 2023
%e Illustration of a(9) = 32:
%e . 12
%e . _ _ _ _ _
%e . |_ _ _ _ _|
%e . _ _ 8
%e . |_ |
%e . |_| _
%e . | |
%e . | |
%e . | | 12
%e . | |
%e . |_|
%e .
%e 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.
%Y Cf. A000203, A008586, A196020, A236104, A237270, A237271, A237593, A244361, A244363, A244370, A244371, A245092, A262626, A279228.
%K nonn,more
%O 1,1
%A _Omar E. Pol_, Dec 11 2016
%E a(29)-a(32) from _Omar E. Pol_, May 04 2023
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