A145580 - OEIS

%I #4 Mar 30 2012 17:25:33

%S 1,1,1,0,1,2,-1,0,2,3,0,-1,0,3,4,1,0,-2,0,4,6,0,1,0,-3,0,6,9,-1,0,2,0,

%T -4,0,9,13,0,-1,0,3,0,-6,0,13,19,1,0,-2,0,4,0,-9,0,19,28

%N Eigentriangle, row sums = A000930

%C Row sums = A000930 starting with offset 1: (1, 1, 2, 3, 4, 6, 9, 13, 19,...).

%C Sum of n-th row terms = rightmost term of next row.

%F Let M = an infinite lower triangular matrix with (1, 1, 0, -1, 0, 1, 0, -1, 0, 1,...) in every column; and X = an infinite lower triangular matrix with A000930 as the main diagonal (offset 1): (1, 1, 2, 3, 4, 6, 9, 13, 19,...) and the rest zeros. Triangle A145580 = M * X.

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 0, 1, 2;

%e -1, 0, 2, 3;

%e 0, -1, 0, 3, 4;

%e 1, 0, -2, 0, 4, 6;

%e 0, 1, 0, -3, 0, 6, 9;

%e -1, 0, 2, 0, -4, 0, 9, 13;

%e 0, -1, 0, 3, 0, -6, 0, 13, 19;

%e 1, 0, -2, 0, 4, 0, -9, 0, 19, 28;

%e ...

%e Row 6 = (1, 0, -2, 0, 4, 6) = termwise products of (1, 0, -1, 0, 1, 1) and (1, 1, 2, 3, 4, 6).

%Y A000930

%K tabl,sign

%O 1,6

%A _Gary W. Adamson_, Oct 13 2008