force transforms and a seemingly nice sequence

[Creighton Dement]

Dear Seqfans, 

Exactly the same iterative process described a few days ago (but applied
to a totally different floretion) seems to lead to at least one nice
sequence.  

Floretion:  + .5'i + 'kk' + .5'jk' , 
Step 1: Transform tesseq by forcing vesseq to take on its values.
Step 2: Step one will have yielded a new sequence- the sequence
"tesforseq". Repeat step one (replacing the words  "tesseq" with
"tesforseq" and "vesseq" with "vesforseq").

***************** 0th iteration *******************

1vesseq: 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 

 
 1tesseq: 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
 
 
 2lesseq: 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3,
 
 
 2jesseq: 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
 


***************** 1st iteration *******************

vesforseq: 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
0, 1 
 
 1tesforseq: -2, 5, -10, 21, -42, 85, -170, 341, -682, 1365, -2730,
5461, 
 
 2lesforseq: 3, -6, 15, -30, 63, -126, 255, -510, 1023, -2046, 4095,
-8190,  
 
 2jesforseq: 1, -2, 5, -10, 21, -42, 85, -170, 341, -682, 1365, -2730,
5461,  

***************** 2nd iteration *******************

1vesforseq: -2, 5, -10, 21, -42, 85, -170, 341, -682, 1365, -2730, 5461,
- 
 
 1tesforseq: -4, 13, -36, 93, -228, 541, -1252, 2845, -6372, 14109, - 
 
 2lesforseq: 3, -12, 39, -108, 279, -684, 1623, -3756, 8535, -19116 
 
 2jesforseq: 1, -4, 13, -36, 93, -228, 541, -1252, 2845, -6372, 14109,  



jesfor yields..
 
%S A000001
1,4,13,36,93,228,541,1252,2845,6372,14109,30948,67357,145636,313117,669924,1427229,3029220,6407965,13514980,28428061,59652324,124897053,260978916,544327453,1133394148,2356266781,4891490532,10140895005,20997617892,43426891549,89717094628
%N A000001 18*a(n) = (3n+1)*2^(n+3) + 9 + (-1)^n
%C A000001 A floretion-generated sequence resulting from particular
transform of A000975.
%H A000001 C. Dement, <a
href="http://www.crowdog.de/13829/home.html">The
Floretions</a>.
%H A000001 C. Dement, <a
href="http://www.crowdog.de/13829/home.html">Force
Transforms</a>.
%F A000001 G.f. 1/((x+1)(1-x)(2x-1)^2) ;
a(n+1) - 2a(n) = A000975(n+2) (n-th number without
              consecutive equal binary digits)
a(n) + a(n+1) = A000337(n+2) ;
a(n+1) - a(n) = A045883(n+2) ;
a(n+2) - a(n) = A001787(n+3) ( Number of edges in n-dimensional
hypercube ) ;
a(n+2) - 2*a(n+1) + a(n) = A059570(n+3) ;
%o A000001 Floretion Algebra Multiplication Program, FAMP Code:
2jesforseq[ + .5'i + 'kk' + .5'jk' ], 1vesforseq(n) =
A000975(n+2)*(-1)^(n+1), ForType: 1A, LoopType: tes (2nd iteration)
%Y A000001 Cf. A000975, A000337, A045883, A001787, A059570.
%O A000001 0
%K A000001 ,easy,nonn,
%A A000001 Creighton Dement (crowdog at crowdog.de), Feb 20 2005

Does anyone have a better name than my "LoopType: tes (2nd iteration)"
given inside the sequence program code? 

Important: if someone is interested in co-authoring some explanations of
force transforms with me (or would just like to help me get some of my
ideas straight) please let me know. Warning- a part of me is very used
to working alone ... so you may have to be overly patient with me as I
have, on top of a lack overall  mathematical knowledge, also developed
all sorts of mental shortcuts along the way. 

Sincerely, 
Creighton

-- Sonja is bigger than me and I am bigger than Sonja! (my 3-year-old
daughter expressing that she and her friend Sonja are exactly the same
height)