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 A342913 #6 Mar 28 2021 19:34:24 %S A342913 1,1,3,1,2,2,5,1,4,2,3,3,7,1,6,2,5,3,4,4,9,1,8,2,7,3,6,4,5,5,11,1,10, %T A342913 2,9,3,8,4,7,5,6,6,13,1,12,2,11,3,10,4,9,5,8,6,7,7,15,1,14,2,13,3,12, %U A342913 4,11,5,10,6,9,7,8,8,17,1,16,2,15,3,14,4,13,5,12,6,11,7 %N A342913 Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < t <= s ordered by decreasing values of s and where k = 1,2,... . %H A342913 <a href="/index/Par#part">Index entries for sequences related to partitions</a> %F A342913 a(n) = k - (k^2 + k - m)*(-1)^n / 2, where k = round(sqrt(m)) and m = 2*floor((n+1-(-1)^n)/2). %F A342913 a(n) = A342769(A103889(n)). %e A342913 [13,1] %e A342913 [11,1] [12,2] %e A342913 [9,1] [10,2] [11,3] %e A342913 [7,1] [8,2] [9, 3] [10,4] %e A342913 [5,1] [6,2] [7,3] [8, 4] [9, 5] %e A342913 [3,1] [4,2] [5,3] [6,4] [7, 5] [8, 6] %e A342913 [1,1] [2,2] [3,3] [4,4] [5,5] [6, 6] [7, 7] %e A342913 2k 2 4 6 8 10 12 14 %e A342913 -------------------------------------------------------------------------- %e A342913 2k Decreasing partitions of 2k %e A342913 -------------------------------------------------------------------------- %e A342913 2 1,1 %e A342913 4 3,1,2,2 %e A342913 6 5,1,4,2,3,3 %e A342913 8 7,1,6,2,5,3,4,4 %e A342913 10 9,1,8,2,7,3,6,4,5,5 %e A342913 12 11,1,10,2,9,3,8,4,7,5,6,6 %e A342913 14 13,1,12,2,11,3,10,4,9,5,8,6,7,7 %e A342913 ... %Y A342913 Cf. A000194, A052928, A103889, A339399, A339443, A342769. %K A342913 nonn %O A342913 1,3 %A A342913 _Wesley Ivan Hurt_, Mar 28 2021