%I #6 Apr 18 2013 09:54:31
%S 1,2,1,0,2,3,-4,0,6,5,-4,-4,0,10,7,4,-4,12,0,14,9,12,4,-12,-20,0,18,
%T 11,4,12,12,-20,-28,0,22,13,-20,4,36,20,-28,-36,0,26,15,-28,-20,12,60,
%U 28,-36,-44,0,30,17
%N Eigentriangle, row sums = (2n + 1).
%C Sum of n-th row terms = rightmost term of next row.
%F Eigentriangle by rows, T(n,k) = A078050(n-k) * X; where X = an infinite lower triangular matrix with (1, 1, 3, 5, 7, 9,...) in the main diagonal and the rest zeros. A078050 is signed: (1, 2, 0, -4, -4, 4, 12, 4, -20, -28,...) = the INVERTi transform of the odd numbers: (1, 3, 5, 7,...).
%e First few rows of the triangle =
%e 1;
%e 2, 1;
%e 0, 2, 3;
%e -4, 0, 6, 5;
%e -4, -4, 0, 10, 7;
%e 4, -4, -12, 0, 14, 9;
%e 12, 4, -12, -20, 0, 18, 11;
%e 4, 12, 12, -20, -28, 0, 22, 13;
%e -20, 4, 36, 20, -28, -36, 0, 26, 15;
%e ...
%e Row 3 = (-4, 0, 6, 5) = (-4*1, 0*1, 3*2, 5*1) = termwise product of (-4, 0, 2, 1) and (1, 1, 3, 5); where (-4, 0, 2, 1) = the first 4 terms of signed A078050 (reversed).
%Y Cf. A005408, A078050.
%K tabl,sign
%O 0,2
%A _Gary W. Adamson_, Sep 11 2008