cp's OEIS Frontend

A244970 Total number of regions after n-th stage in the diagram of the symmetric representation of sigma on the four quadrants.

%I A244970 #26 Dec 31 2020 11:11:15
%S A244970 1,2,6,7,11,12,16,17,25,29,33,34,38,42,50,51,55,56,60,61,73,77,81,82,
%T A244970 90,94,106,107,111,112,116,117,129,133,141,142,146,150,162,163,167,
%U A244970 168,172,176,184,188,192,193,201,209,221,225,229,230,242,243,255,259,263,264
%N A244970 Total number of regions after n-th stage in the diagram of the symmetric representation of sigma on the four quadrants.
%C A244970 Partial sums of A244971.
%C A244970 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.
%C A244970 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).
%C A244970 a(n) is also the total number of terraces of the stepped pyramid with n levels described in A244050. - _Omar E. Pol_, Apr 20 2016
%e A244970 Illustration of the structure after 15 stages (contains 50 regions):
%e A244970 .
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%e A244970 .
%e A244970 The diagram is also the top view of the stepped pyramid with 15 levels described in A244050. - _Omar E. Pol_, Apr 20 2016
%Y A244970 Cf. A000203, A004125, A024916, A196020, A235791, A236104, A237270, A237271, A237590, A237591, A237593, A239050, A239660, A239931-A239934, A243980, A244050, A244360-A244363, A244370, A244371, A244971, A245092.
%K A244970 nonn
%O A244970 1,2
%A A244970 _Omar E. Pol_, Jul 08 2014