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Triangle, A004736 * A127899.
0

%I #5 Jan 15 2013 09:23:10

%S 1,0,2,-1,1,3,-2,0,2,4,-3,-1,1,3,5,-4,-2,0,2,4,6,-5,-3,-1,1,3,5,7,-6,

%T -4,-2,0,2,4,6,8,-7,-5,-3,-1,1,3,5,7,9,-8,-6,-4,-2,0,2,4,6,8,10

%N Triangle, A004736 * A127899.

%C Row sums = n A127899 * A004736 = A002024

%F A004736 * A127899 as infinite lower triangular matrices; where A004736 = (1; 2,1; 3,2,1;...).

%F From _Boris Putievskiy_, Jan 15 2013: (Start)

%F a(n) = 2*A000027(n)-A002024(n)^2, n > 0,

%F a(n) = 2*n-(t+1)^2, where t = floor((-1+sqrt(8*n-7))/2) n > 0. (End)

%e First few rows of the triangle are:

%e 1;

%e 0, 2;

%e -1, 1, 3;

%e -2, 0, 2, 4;

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

%e -4, -2, 0, 2, 4, 6;

%e -5, -3, -1, 1, 3, 5, 7;

%e ...

%Y Cf. A127899, A004736, A002024.

%K tabl,sign

%O 0,3

%A _Gary W. Adamson_, Feb 09 2007