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%I #10 Jul 10 2021 03:02:16

%S 1,-1,2,2,-1,3,-2,3,-1,4,3,-2,4,-1,5,-3,4,-2,5,-1,6,4,-3,5,-2,6,-1,7,

%T -4,5,-3,6,-2,7,-1,8,5,-4,6,-3,7,-2,8,-1,9,-5,6,-4,7,-3,8,-2,9,-1,10

%N A002260 * A097807.

%C Row sums = A008794: (1, 1, 4, 4, 9, 9, 16, 16, ...).

%C Unsigned row sums = the triangular sequence, A000217: (1, 3, 6, 10, ...) by virtue of the fact that each row is a permutation of the natural numbers.

%C A128179 = A097807 * A002260.

%F A002260 * A097807 as infinite lower triangular matrices.

%F From _Franklin T. Adams-Watters_, Apr 12 2011: (Start)

%F T(n,k) = (2k - 1 + (-1)^(n-k)*(2n+1))/4.

%F |T(n,k)| = (2n+1 + (-1)^(n-k)*(2k-1))/4. (End)

%e Triangle begins:

%e 1;

%e -1, 2;

%e 2, -1, 3;

%e -2, 3, -1, 4;

%e 3, -2, 4, -1, 5;

%e -3, 4, -2, 5, -1, 6;

%e 4, -3, 5, -2, 6, -1, 7;

%e ...

%o (PARI) T(n,k)=(2*k-1+(-1)^(n-k)*(2*n+1))/4 \\ _Franklin T. Adams-Watters_, Apr 12 2011

%Y Cf. A002260, A097807, A008794, A128179.

%K tabl,sign

%O 1,3

%A _Gary W. Adamson_, Feb 17 2007