

A077606


Left differencing matrix, D, by antidiagonals.


1



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, n1)=1, D(n, n)=1, else D(n, k)=0.
As a sequence, a(2k^22k+1) = 1, a(2k^2) = 1, otherwise a(n) = 0.  Franklin T. AdamsWatters, 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
0 0 0 1 1


CROSSREFS

Cf. A077605.
Cf. A001844, A001105.
Sequence in context: A113429 A133100 A216230 * A004601 A267418 A263919
Adjacent sequences: A077603 A077604 A077605 * A077607 A077608 A077609


KEYWORD

easy,sign,tabl


AUTHOR

Clark Kimberling, Nov 11 2002


STATUS

approved



