OFFSET
0,5
COMMENTS
Right border = A000587, the Rao Uppuluri-Carpenter numbers, with different signs: (1, 1, 0, 1, 1, 2, 9, -9, 50, -267, -413, -2180,...).
Row sums = the same sequence shifted: (1, 0, 1, 1, 2, 9,...).
Let A = the self-inverse triangle, A118433. Shift the triangle down one place placing "1" at (0,0). Lim_{n->oo} A^n, = a signed version B of the Rao Uppuluri-Carpenter numbers (A000587), as follows: (1, 1, 0, 1, 1, 2, 9, -9, 50, -267, -413, -2180,...). This triangle = (A * (an infinite lower triangular matrix with B as the main diagonal and the rest zeros)). These operations are equivalent to (by rows), taking termwise products of A118433 row terms and B, the signed version of the Rao Uppuluri-Carpenter numbers.
EXAMPLE
First few rows of the triangle =
1;
1, -1;
-1, 2, 0;
-1, 3, 0, -1,
1, -4, 0, 4, 1;
1, -5, 0, 10, 5, -2;
-1, 6, 0, -20, -15, 12, 9;
-1, 7, 0, -35, -35, 42, 63, 9;
1, -8, 0, 56, 70, -112, -252, -72, 50;
1, -9, 0, 84, 126, -252, -756, -324, 450, 267;
-1, 10, 0, -120, -210, 504, 1890, 1080, -2250, -2670, -413;
...
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Sep 13 2008
STATUS
approved