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 A361442 #14 Mar 14 2023 03:44:10
%S A361442 0,1,-1,2,-3,4,3,-5,8,-12,5,-8,13,-21,33,6,-11,19,-32,53,-86,-2,-4,15,
%T A361442 -34,66,-119,205,9,-7,11,-26,60,-126,245,-450,10,-19,26,-37,63,-123,
%U A361442 249,-494,944,7,-17,36,-62,99,-162,285,-534,1028,-1972
%N A361442 Infinite triangle T(n, k), n, k >= 0, read and filled by rows the greedy way with distinct integers such that for any n, k >= 0, T(n, k) + T(n+1, k) + T(n+1, k+1) = 0; each term is minimal in absolute value and in case of a tie, preference is given to the positive value.
%C A361442 Will every integer appear in the triangle?
%H A361442 Rémy Sigrist, <a href="/A361442/b361442.txt">Table of n, a(n) for n = 0..10010</a>
%H A361442 Rémy Sigrist, <a href="/A361442/a361442.png">Colored representation of the first 500 rows</a> (the color is function of the sign of T(n, k))
%H A361442 Rémy Sigrist, <a href="/A361442/a361442.gp.txt">PARI program</a>
%F A361442 T(n, 0) = A361443(n).
%F A361442 T(n, k) = (-1)^k * Sum_{i = 0..k} binomial(k, i) * T(n-i, 0).
%e A361442 Triangle begins:
%e A361442 0
%e A361442 1 -1
%e A361442 2 -3 4
%e A361442 3 -5 8 -12
%e A361442 5 -8 13 -21 33
%e A361442 6 -11 19 -32 53 -86
%e A361442 -2 -4 15 -34 66 -119 205
%e A361442 9 -7 11 -26 60 -126 245 -450
%e A361442 10 -19 26 -37 63 -123 249 -494 944
%e A361442 7 -17 36 -62 99 -162 285 -534 1028 -1972
%o A361442 (PARI) See Links section.
%Y A361442 Cf. A152920, A361443.
%K A361442 sign,tabl
%O A361442 0,4
%A A361442 _Rémy Sigrist_, Mar 12 2023