sequences based on ab-cd

[Rainer Rosenthal]

The well known determinant expression  ab-cd
inspired three sequences

S1:  1, 1, 1, 1, ... a, b, c, d, ab-cd, ...
S2:  1, 1, 1, 1, ... a, b, c, d, ac-bd, ...
S3:  1, 1, 1, 1, ... a, b, c, d, ad-bc, ...

which look funny (and new):

S1: 1,1,1,1,0,1,1,-1,1,2,-3,5,17,-91,1532,139497,-213710951,...
S2: 1,1,1,1,0,1,-1,1,-1,0,1,1,-1,1,-2,-1,3,5,-1,-2,7,-3,-13,
    97,200,2309,-226573,45538573,...
S3: 1,1,1,1,0,-1,-1,-1,-1,0,-1,1,-1,1,0,1 (last 5 repeating)

Until now I never submitted any sequences with negative signs.
And I do not know whether S3 is allowed.

Would some other seqFan please enter these, so that I could
learn, how to to do it in the future? Benoit?
I am not really lazy but I don't want to spoil these little
sequences.

With best regards
Rainer Rosenthal
r.rosenthal at web.de