%I #17 Apr 17 2014 10:57:26
%S 1,4,9,29,55,157,277,669,1212,2555,4459,9048
%N Sum of all region numbers of all parts of the last section of the set of partitions of n.
%C Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.
%C The last section of the set of partitions of n is also the n-th section of the set of partitions of any integer >= n. - _Omar E. Pol_, Apr 07 2014
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%e For n = 6 the four regions of the last section of 6 are [2], [4, 2], [3], [6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] therefore the "region numbers" are [8], [9, 9], [10], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11]. The sum of all region numbers is a(6) = 8+2*9+10+11^2 = 8+18+10+121 = 157, see below:
%e --------------------------------------------
%e . Last section Sum of
%e . of the set of Region region
%e k partitions of 6 numbers numbers
%e --------------------------------------------
%e 11 6 11 11
%e 10 3+3 10,11 21
%e 9 4 +2 9, 11 20
%e 8 2+2 +2 8,9, 11 28
%e 7 1 11 11
%e 6 1 11 11
%e 5 1 11 11
%e 4 1 11 11
%e 3 1 11 11
%e 2 1 11 11
%e 1 1 11 11
%e --------------------------------------------
%e Total sum of region numbers is a(6) = 157
%Y Row sums of triangle A210966. Partial sums give A210972.
%Y Cf. A135010, A138121, A194446, A182703, A206437, A210971.
%K nonn,more
%O 1,2
%A _Omar E. Pol_, Jul 01 2012