# [seqfan] Bear's paw sequence

Jeremy Gardiner jeremy.gardiner at btinternet.com
Sun Aug 29 19:34:04 CEST 2010

```Is there a place for sequences related to geometric designs in the OEIS?

The following sequence was inspired by the traditional Bear's Paw quilt
design:

http://www.jeremy.gardiner.btinternet.co.uk/maths/bears_paw.gif

1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,-5,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,
-1,0,-5,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,5,0,1,-1,-1,0,1,-1,-1,0,0,-1,-
1,1,0,-1,-1,1,0,5

This geometric design is produced by drawing straight lines starting from
the origin such that each pair of terms in the sequence gives successive
differences in x and y coordinates.

There is an interesting history of this design here:

http://www.womenfolk.com/quilt_pattern_history/bearspaw.htm

Changing the 5's in this sequence to 1's produces an octagonal cross design:

http://www.jeremy.gardiner.btinternet.co.uk/maths/octagon_cross.gif

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

Alternative substitutions for 5's (and/or sign change) produces these other
interesting designs:

http://www.jeremy.gardiner.btinternet.co.uk/maths/diamond.gif

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

http://www.jeremy.gardiner.btinternet.co.uk/maths/triangles.gif

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

http://www.jeremy.gardiner.btinternet.co.uk/maths/bears_paw_cross.gif

1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,5,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,-
1,0,5,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,-5,0,1,-1,-1,0,1,-1,-1,0,0,-1,-1
,1,0,-1,-1,1,0,-5

Doubtless these designs and the corresponding sequences have been studied
before by someone - does anybody know of references to these?

Jeremy

```