A077606 - OEIS

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A077606

Left differencing matrix, D, by antidiagonals.

1, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

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OFFSET

1,1

COMMENTS

If v is a sequence written as a column vector, then Dv is the sequence of first differences of v. The inverse of D is the left summing matrix; the transpose of D is the right differencing matrix.

LINKS

Table of n, a(n) for n=1..108.

C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.

FORMULA

D(n, n-1)=-1, D(n, n)=1, else D(n, k)=0.

As a sequence, a(2k^2-2k+1) = 1, a(2k^2) = -1, otherwise a(n) = 0. - Franklin T. Adams-Watters, Jan 12 2007

EXAMPLE

Northwest corner:

1 0 0 0 0

-1 1 0 0 0

0 -1 1 0 0

0 0 -1 1 0