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 A285891 #40 Nov 04 2019 08:55:24
%S A285891 1,2,3,3,4,0,5,5,6,0,6,7,7,0,8,0,0,9,9,9,10,0,0,10,11,11,0,0,12,0,12,
%T A285891 0,13,13,0,0,14,0,0,14,15,15,15,0,15,16,0,0,0,0,17,17,0,0,0,18,0,18,
%U A285891 18,0,19,19,0,0,0,20,0,0,0,20,21,21,21,0,0,21,22,0,0,22,0,0,23,23,0,0,0,0,24,0,24,0,0,0
%N A285891 Triangle read by rows: T(n,k) = n*A237048(n,k).
%C A285891 Conjecture: T(n,k) = n, is also the sum of the parts of the partition of n into k consecutive parts, if such a partition exists, otherwise T(n,k) = 0.
%e A285891 Triangle begins:
%e A285891 1;
%e A285891 2;
%e A285891 3, 3;
%e A285891 4, 0;
%e A285891 5, 5;
%e A285891 6, 0, 6;
%e A285891 7, 7, 0;
%e A285891 8, 0, 0;
%e A285891 9, 9, 9;
%e A285891 10, 0, 0, 10;
%e A285891 11, 11, 0, 0;
%e A285891 12, 0, 12, 0;
%e A285891 13, 13, 0, 0;
%e A285891 14, 0, 0, 14;
%e A285891 15, 15, 15, 0, 15;
%e A285891 16, 0, 0, 0, 0;
%e A285891 17, 17, 0, 0, 0;
%e A285891 18, 0, 18, 18, 0;
%e A285891 19, 19, 0, 0, 0;
%e A285891 20, 0, 0, 0, 20;
%e A285891 21, 21, 21, 0, 0, 21;
%e A285891 22, 0, 0, 22, 0, 0;
%e A285891 23, 23, 0, 0, 0, 0;
%e A285891 24, 0, 24, 0, 0, 0;
%e A285891 25, 25, 0, 0, 25, 0;
%e A285891 26, 0, 0, 26, 0, 0;
%e A285891 27, 27, 27, 0, 0, 27;
%e A285891 28, 0, 0, 0, 0, 0, 28;
%e A285891 ...
%o A285891 (PARI) t(n, k) = if (k % 2, (n % k) == 0, ((n - k/2) % k) == 0); \\ A237048
%o A285891 tabf(nn) = {for (n=1, nn, for (k=1, floor((sqrt(1+8*n)-1)/2), print1(n*t(n, k), ", "); ); print(); ); } \\ _Michel Marcus_, Nov 04 2019
%Y A285891 Row sums give A245579.
%Y A285891 Row n has length A003056(n).
%Y A285891 Column k starts in row A000217(k).
%Y A285891 The number of positive terms in row n is A001227(n), the number of partitions of n into consecutive parts.
%Y A285891 Cf. A196020, A211343, A235791, A236104, A237048, A237591, A237593, A245579, A285900, A285914, A286013.
%K A285891 nonn,tabf
%O A285891 1,2
%A A285891 _Omar E. Pol_, May 02 2017