%I #10 Mar 02 2024 15:53:46
%S 1,0,1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,0,-1,0,
%T 1,0,-1,0,1,1,0,-1,0,1,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,
%U 0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1
%N Triangle read by rows. T(n, k) = 0 if n - k is odd otherwise if 4 divides n - k then 1 otherwise -1.
%C Signed version of A128174.
%H Paolo Xausa, <a href="/A369736/b369736.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of the triangle, flattened).
%p T := (n, k) -> if irem(n - k, 2) = 1 then 0 elif irem(n - k, 4) = 0 then 1 else -1 fi: seq(seq(T(n, k), k = 0..n), n = 0..11);
%t A369736[n_, k_] := Which[OddQ[n-k], 0, Divisible[n-k, 4], 1, True, -1];
%t Table[A369736[n, k], {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Mar 02 2024 *)
%Y Row sums: A133872 (period 4: repeat [1, 1, 0, 0]).
%Y Alternating row sums: A219977 (period 4: repeat [1, -1, 0, 0]).
%Y Central terms: A056594 (period 4: repeat [1, 0, -1, 0]).
%Y Cf. A128174.
%K sign,tabl,easy
%O 0
%A _Peter Luschny_, Mar 02 2024