This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A210969 #17 Apr 17 2014 10:57:26 %S A210969 1,4,9,29,55,157,277,669,1212,2555,4459,9048 %N A210969 Sum of all region numbers of all parts of the last section of the set of partitions of n. %C A210969 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 A210969 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 A210969 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a> %e A210969 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 A210969 -------------------------------------------- %e A210969 . Last section Sum of %e A210969 . of the set of Region region %e A210969 k partitions of 6 numbers numbers %e A210969 -------------------------------------------- %e A210969 11 6 11 11 %e A210969 10 3+3 10,11 21 %e A210969 9 4 +2 9, 11 20 %e A210969 8 2+2 +2 8,9, 11 28 %e A210969 7 1 11 11 %e A210969 6 1 11 11 %e A210969 5 1 11 11 %e A210969 4 1 11 11 %e A210969 3 1 11 11 %e A210969 2 1 11 11 %e A210969 1 1 11 11 %e A210969 -------------------------------------------- %e A210969 Total sum of region numbers is a(6) = 157 %Y A210969 Row sums of triangle A210966. Partial sums give A210972. %Y A210969 Cf. A135010, A138121, A194446, A182703, A206437, A210971. %K A210969 nonn,more %O A210969 1,2 %A A210969 _Omar E. Pol_, Jul 01 2012