A244970 - OEIS

A244970

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

1, 2, 6, 7, 11, 12, 16, 17, 25, 29, 33, 34, 38, 42, 50, 51, 55, 56, 60, 61, 73, 77, 81, 82, 90, 94, 106, 107, 111, 112, 116, 117, 129, 133, 141, 142, 146, 150, 162, 163, 167, 168, 172, 176, 184, 188, 192, 193, 201, 209, 221, 225, 229, 230, 242, 243, 255, 259, 263, 264

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Partial sums of A244971.

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.

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).

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

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

Illustration of the structure after 15 stages (contains 50 regions):

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The diagram is also the top view of the stepped pyramid with 15 levels described in A244050. - Omar E. Pol, Apr 20 2016

CROSSREFS

Cf. A000203, A004125, A024916, A196020, A235791, A236104, A237270, A237271, A237590, A237591, A237593, A239050, A239660, A239931-A239934, A243980, A244050, A244360-A244363, A244370, A244371, A244971, A245092.

Sequence in context: A221847 A283766 A047216 * A242330 A376131 A039568

Adjacent sequences: A244967 A244968 A244969 * A244971 A244972 A244973

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jul 08 2014

STATUS

approved