login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)