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 A342769 #9 May 09 2021 12:56:29 %S A342769 1,1,1,3,2,2,1,5,2,4,3,3,1,7,2,6,3,5,4,4,1,9,2,8,3,7,4,6,5,5,1,11,2, %T A342769 10,3,9,4,8,5,7,6,6,1,13,2,12,3,11,4,10,5,9,6,8,7,7,1,15,2,14,3,13,4, %U A342769 12,5,11,6,10,7,9,8,8,1,17,2,16,3,15,4,14,5,13,6,12,7 %N A342769 Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < s <= t ordered by increasing values of s and where k = 1,2,... . %H A342769 <a href="/index/Par#part">Index entries for sequences related to partitions</a> %F A342769 a(n) = k + (k^2 + k - m)*(-1)^n / 2, where k = round(sqrt(m)) and m = 2*floor((n+1)/2). %F A342769 a(n) = A342913(A103889(n)). - _Wesley Ivan Hurt_, May 09 2021 %e A342769 [1,13] %e A342769 [1,11] [2,12] %e A342769 [1,9] [2,10] [3,11] %e A342769 [1,7] [2,8] [3, 9] [4,10] %e A342769 [1,5] [2,6] [3,7] [4, 8] [5, 9] %e A342769 [1,3] [2,4] [3,5] [4,6] [5, 7] [6, 8] %e A342769 [1,1] [2,2] [3,3] [4,4] [5,5] [6, 6] [7, 7] %e A342769 2k 2 4 6 8 10 12 14 %e A342769 -------------------------------------------------------------------------- %e A342769 2k Nondecreasing partitions of 2k %e A342769 -------------------------------------------------------------------------- %e A342769 2 1,1 %e A342769 4 1,3,2,2 %e A342769 6 1,5,2,4,3,3 %e A342769 8 1,7,2,6,3,5,4,4 %e A342769 10 1,9,2,8,3,7,4,6,5,5 %e A342769 12 1,11,2,10,3,9,4,8,5,7,6,6 %e A342769 14 1,13,2,12,3,11,4,10,5,9,6,8,7,7 %e A342769 ... %Y A342769 Cf. A000194, A052928, A103889, A339399, A339443, A342913. %K A342769 nonn,tabf %O A342769 1,4 %A A342769 _Wesley Ivan Hurt_, Mar 21 2021