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%I #10 Mar 06 2022 00:13:00
%S 1,-2,-5,3,0,5,-4,-7,-2,-9,5,2,7,0,9,-6,-9,-4,-11,-2,-13,7,4,9,2,11,0,
%T 13,-8,-11,-6,-13,-4,-15,-2,-17,9,6,11,4,13,2,15,0,17,-10,-13,-8,-15,
%U -6,-17,-4,-19,-2,-21,11,8,13,6,15,4,17,2,19,0,21
%N Triangle read by rows: T(n,k) = (-1)^(n-1)*n + (-1)^(k-1)*k - 1, 1 <= k <= n.
%C Row sums = A132899: (1, -7, 8, -22, 23, -45, ...).
%H Andrew Howroyd, <a href="/A132898/b132898.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%e First few rows of the triangle:
%e 1;
%e -2, -5;
%e 3, 0, 5;
%e -4, -7, -2, -9;
%e 5, 2, 7, 0, 9;
%e -6, -9, -4, -11, -2, -13;
%e 7, 4, 9, 2, 11, 0, 13;
%e -8, -11, -6, -13, -4, -15, -2, -17;
%e 9, 6, 11, 4, 13, 2, 15, 0, 7;
%e ...
%e T(5,3) = 7 = S(5) + S(3) = 5 + 3 - 1.
%o (PARI) T(n,k) = if(k<=n, (-1)^(n-1)*n + (-1)^(k-1)*k - 1, 0); \\ _Andrew Howroyd_, Sep 01 2018
%Y Row sums are A132899.
%Y Cf. A127648.
%K tabl,sign
%O 1,2
%A _Gary W. Adamson_, Sep 03 2007
%E Name clarified and terms a(56) and beyond from _Andrew Howroyd_, Sep 01 2018
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