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Eigentriangle, row sums = (2n + 1).
2

%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