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

[creigh at o2online.de]

Hello again, 

The sequence Simon mentioned is also in the same batch of "chu's group" symmetries 
for the floretion - 0.5'j - 0.5'k - 0.5j' - 0.5k' + 1'jj' + 0.5'kk' - 0.5'ik' 
- 0.5'ki' - 0.5e  (see chuseq[J]). My experience is that if two sequences 
are in the same batch for a single floretion,
the (denominators of the) generating functions will often look quite similar 
if not the same (static symmetries only).


(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 
********************************
Hello, 

just a note about the sequence, 

here is another one, : 

[((n+1)/2)], n=1,2,3,4,... 

which is 1,1,2,2,3,3,4,4,5,5,6,6,... and [ ] is the floor function. 

It also has this generating function : 1/(x+1)/(x-1)^2 
which is a 3rd order recurrence too. 

The one you mention is nicer I must say since the terms 
that represent 2 * N are mixed up. 

Simon Plouffe