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 A293670 #9 Nov 11 2019 00:50:28
%S A293670 1,-1,0,2,1,0,2,-1,1,2,0,3,1,1,2,0,3,-1,2,2,1,3,0,4,1,2,2,1,3,0,4,-1,
%T A293670 3,2,2,3,1,4,0,5,1,3,2,2,3,1,4,0,5,-1,4,2,3,3,2,4,1,5,0,6,1,4,2,3,3,2,
%U A293670 4,1,5,0,6,-1,5,2,4,3,3,4,2,5,1,6,0,7,1,5,2,4,3,3,4,2,5,1,6,0,7,-1,6,2,5,3,4,4,3,5,2,6,1,7,0,8,1,6,2,5,3,4,4,3,5,2,6,1,7,0,8,-1,7,2,6,3,5,4,4,5,3,6,2,7,1,8,0,9,1,7,2,6,3,5,4,4,5,3,6,2,7,1,8,0,9,-1
%N A293670 Square array made of (W, N, S, E) quadruplets read by antidiagonals. Numeric structure of an anamorphosis of A002024 (see comments).
%C A293670 Numeric characterization:
%C A293670 Row n is the value of a list after n iterations of the following algorithm:
%C A293670 - start with an empty list (assimilable to row number 0)
%C A293670 - Iteration n consists of
%C A293670 -- if n is odd, appending 1 to the left of the list and -1 to the right;
%C A293670 -- if n is even, replacing each value in the list by its complement to n/2.
%C A293670 Underlying definition and interest: this sequence represents a square array in which each cell is a structure made of 4 values arranged in W/N/S/E fashion. These values are twice the areas of elementary right triangles that enter the composition of quadrilaterals delimited by two families of lines, with the following equations:
%C A293670 - for m = 1, 2, 3, ...: y = mx - (m-1)^2 {x <= m-1}
%C A293670 - for n = -1, 0, 1, ...: y = -nx - (n+1)^2 {x >= 1-n}
%C A293670 Globally these quadrilaterals form an anamorphosis of A002024. See provided link for explanations and illustrations.
%H A293670 Luc Rousseau, <a href="/A293670/a293670_1.pdf">Relation between A293670 and A002024 - Numeric structure of an anamorphosis</a>
%e A293670 Array begins (characterization)(x stands for -1):
%e A293670 1 x
%e A293670 0 2
%e A293670 1 0 2 x
%e A293670 1 2 0 3
%e A293670 1 1 2 0 3 x
%e A293670 2 2 1 3 0 4
%e A293670 1 2 2 1 3 0 4 x
%e A293670 3 2 2 3 1 4 0 5
%e A293670 1 3 2 2 3 1 4 0 5 x
%e A293670 4 2 3 3 2 4 1 5 0 6
%e A293670 1 4 2 3 3 2 4 1 5 0 6 x
%e A293670 5 2 4 3 3 4 2 5 1 6 0 7
%e A293670 1 5 2 4 3 3 4 2 5 1 6 0 7 x
%e A293670 Or (definition)(to be read by antidiagonals):
%e A293670 x x x x
%e A293670 1 2 2 3 3 4 4 5 ...
%e A293670 0 0 0 0
%e A293670 0 0 0 0
%e A293670 1 2 2 3 3 4 4 5 ...
%e A293670 1 1 1 1
%e A293670 1 1 1 1
%e A293670 1 2 2 3 3 4 4 5 ...
%e A293670 2 2 2 2
%e A293670 2 2 2 2
%e A293670 1 2 2 3 3 4 4 5 ...
%e A293670 3 3 3 3
%e A293670 3 3 3 3
%e A293670 1 2 2 3 3 4 4 5 ...
%e A293670 4 4 4 4
%e A293670 ...
%o A293670 (PARI)
%o A293670 evolve(L,n)=if(n%2==1,listinsert(L,1,1);listinsert(L,-1,#L+1),L=apply(v->n/2-v,L));L
%o A293670 N=30;L=List();for(n=1,N,L=evolve(L,n);for(i=1,#L,print1(L[i],", "));print())
%Y A293670 Cf. A293578, A002024.
%K A293670 sign,tabf
%O A293670 1,4
%A A293670 _Luc Rousseau_, Oct 14 2017