Problems with sequence (A090591) signs...

[creigh at o2online.de]

Problems with signs...

Apparently, the following equations hold (see below)

| vesseq(n) | = | A090591(n+1) | =  | (1/3)*lesseq(n+1) | =  | (1/2)*jesseq(n+1) |

| tesseq(n)  | = | A090590(n+1) |

    
A090590  (1,1) entry of powers of the orthogonal design shown below.
A090591, (1,2) entry of powers of the orthogonal design shown below:
           +1 +1 +1 +1 +1 +1 +1 +1
           -1 +1 +1 -1 +1 -1 -1 +1
           -1 -1 +1 +1 +1 +1 -1 -1
           -1 +1 -1 +1 +1 -1 +1 -1
           -1 -1 -1 -1 +1 +1 +1 +1
           -1 +1 -1 +1 -1 +1 -1 +1
           -1 +1 +1 -1 -1 +1 +1 -1
           -1 -1 +1 +1 -1 -1 +1 +1

The problem is: A090591 and A090590 are both signed sequences whose signs do 
not coincide with my sequences. On one hand, it would be nice to use the 
standard jes + les + tes = ves formula, for example, to relate both sequences 
with each other. On the other hand,
if a simple function vesseq(n)  |->  A090591(n+1)  cannot be found, I don't 
see how the formula can be used.

Does anyone see a way that the formula may be used without submitting any 
new sequences?
 
Sincerely, 
Creighton 

 Results for the floretion:   
 **********************************************************  
  + 3'i - 1'k - 1'jj' - 1'ji' - 1'jk' - 1e 
 ********************************************************** 
 
 (squaring symmetries:) 
  
vesseq: -2, -4, 24, -16, -160, 448, 384, -4352, 5632, 23552, -92160,  
tesseq: -1, -6, 20, 8, -176, 288, 832, -3968, 1280, 29184, -68608,   lesseq: 
-3, 6, 12, -72, 48, 480, -1344, -1152, 13056, -16896, -70656,  
jesseq: 2, -4, -8, 48, -32, -320, 896, 768, -8704, 11264, 47104,   
 
 identity: ves = jes + les + tes  
 
 (Emmy's Three, subgroup symmetries:) 
  
 em[I]seq: 0, -8, 16, 32, -192, 128, 1280, -3584, -3072, 34816, -45056, -188416, 
737280, 32768 
 em[I*]seq: -2, 4, 8, -48, 32, 320, -896, -768, 8704, -11264, -47104, 184320, 
8192, -1490944
 
 em[J]seq: -4, 0, 32, -64, -128, 768, -512, -5120, 14336, 12288, -139264, 180224, 
753664, -2949120, -131072 
 em[J*]seq: 2, -4, -8, 48, -32, -320, 896, 768, -8704, 11264, 47104, -184320, 
-8192, 1490944, -2916352
 
 em[K]seq: -2, -4, 24, -16, -160, 448, 384, -4352, 5632, 23552, -92160, -4096, 
745472, -1458176, -3047424 
 em[K*]seq: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
 
 famseq: -2, -4, 24, -16, -160, 448, 384, -4352, 5632, 23552, -92160, -4096, 
745472, -1458176, -3047424
 fam*seq: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 
 
 identities: em[I] + em[J] + em[K] = 2*fam + ves  
 em[I] + em[I*] = em[J] + em[J*] = em[K] + em[K*] = fam + fam* = ves