2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, . . .

[creigh at o2online.de]

Dear Henry, 

Your sequence looks a lot like achu[I]+tesseq, below. It would be my
pleasure to inform you of the details of this (static) symmetry if 
you wish.

Sincerely, 
Creighton 

Results for the floretion:  G*M
 **********************************************************  
  - 0.5'j - 0.5'k - 0.5j' - 0.5k' + 1'jj' + 0.5'kk' - 0.5'ik' - 0.5'ki' 
- 0.5e 
 **********************************************************  
G = .5 'kk' + .5 'ij' + .5 'ji' + .5 e
M = 0.0 'i - 0.5 'j - 0.5 'k + 0.0 i' - 0.5 j' - 0.5 k' + 0.0 'ii' + 1.0 
'jj' + 0.5 'kk' + 0.0 'ij' - 0.5 'ik' + 0.0 'ji' + 0.0 'jk' - 0.5 'ki' + 
0.0 'kj' - 0.5 e
 
Invariant to swap operator: yes
G commutes with M: no
 
 
 ****************************  Static Symmetries  *************************************************************************************************************** 
 
 (squaring symmetries:) 
  
 vesseq: -2, 9, -14, 25, -34, 49, -62, 81, -98, 121, -142, 169, -194, 225, 
-254, 289 
 2tesseq: -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2 
 2lesseq: 1, 8, -15, 32, -47, 72, -95, 128, -159, 200, -239, 288, -335, 
392, -447, 512 
 jesseq: -2, 4, -6, 8, -10, 12, -14, 16, -18, 20, -22, 24, -26, 28, -30, 
32 
 
 identity: ves = jes + les + tes  
 
  
 (Chu's group, subgroup symmetries, incomplete:) 
  
 chuseq[J]: 0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8 
 (signed)chuseq[J]: 0, 3, -7, 14, -22, 33, -45, 60, -76, 95, -115, 138, 
-162, 189, -217, 248 
 2chutesseq[J]: -1, 4, -3, 6, -5, 8, -7, 10, -9, 12, -11, 14, -13, 16, 
-15, 18 
 2achuseq[J]: -3, 14, -25, 44, -63, 90, -117, 152, -187, 230, -273, 324, 
-375, 434, -493, 560 
 achu[J]+tesseq: -2, 8, -13, 23, -32, 46, -59, 77, -94, 116, -137, 163, 
-188, 218, -247, 281 
 2achu[K]+tesseq: -1, 6, -5, 10, -9, 14, -13, 18, -17, 22, -21, 26, -25, 
30, -29, 34 
 achu[I]+tesseq: 1, 0, 2, -1, 3, -2, 4, -3, 5, -4, 6, -5, 7, -6, 8, -7