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A132898 Triangle read by rows: T(n,k) = (-1)^(n-1)*n + (-1)^(k-1)*k - 1, 1 <= k <= n.

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