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 A210972 #16 Mar 11 2014 01:34:20 %S A210972 1,5,14,43,98,255,532,1201,2413,4968,9427,18475 %N A210972 Sum of all region numbers of all parts of all partitions of n. %C A210972 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. %H A210972 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a> %e A210972 For n = 5 we have: %e A210972 --------------------------------------------------- %e A210972 . Two arrangements %e A210972 k of the partitions of 5 %e A210972 --------------------------------------------------- %e A210972 7 [5] [5] %e A210972 6 [3+2] [3+2] %e A210972 5 [4+1] [4 +1] %e A210972 4 [2+1+1] [2+2 +1] %e A210972 3 [3+1+1] [3 +1 +1] %e A210972 2 [2+1+1+1] [2+1 +1 +1] %e A210972 1 [1+1+1+1+1] [1+1+1 +1 +1] %e A210972 --------------------------------------------------- %e A210972 . Two arrangements %e A210972 . of the region numbers Sum of %e A210972 k of the partitions of 5 zone k %e A210972 --------------------------------------------------- %e A210972 7 [7] [7] 7 %e A210972 6 [6,7] [6,7] 13 %e A210972 5 [5,7] [5, 7] 12 %e A210972 4 [4,5,7] [4,5, 7] 16 %e A210972 3 [3,5,7] [3, 5, 7] 15 %e A210972 2 [2,3,5,7] [2,3, 5, 7] 17 %e A210972 1 [1,2,3,5,7] [1,2,3, 5, 7] 18 %e A210972 --------------------------------------------------- %e A210972 The total sum is a(5) = 1+2^2+3^2+4+5^2+6+7^2 = 1+4+9+4+25+6+49 = 18+17+15+16+12+13+7 = 98. %Y A210972 Partial sums of A210969. Row sums of triangle A210971. %Y A210972 Cf. A135010, A138121, A182703, A194446, A210437, A210966. %K A210972 nonn,more %O A210972 1,2 %A A210972 _Omar E. Pol_, Jun 30 2012