A comment regarding NSW / Pell numbers / Chebyshev polynomials.

[Creighton Dement]

Dear Seqfans, 

Need some help in formulating a comment... 

I get the results (another "force transform of the zero-sequence" ) 

 2lesfor(pos)seq: 3, 1, 17, 5, 99, 29, 577, 169, 3363, 985, 19601, 5741,
114243, 33461, 665857, 195025, 3880899,  1136689, 22619537, 6625109,
131836323, 38613965, 768398401, 225058681, 4478554083, 1311738121,
26102926097,  

2lesfor(neg)seq:0, -7, -2, -41, -12, -239, -70, -1393, -408, -8119,
-2378, -47321, -13860, -275807, -80782, -1607521,  -470832, -9369319,
-2744210, -54608393, -15994428, -318281039, -93222358, -1855077841,
-54333972, -10812186007,  

 2lesforseq: 3, -6, 15, -36, 87, -210, 507, -1224, 2955, -7134, 17223,
-41580, 100383, -242346, 585075, -1412496,  3410067, -8232630, 19875327,
-47983284, 115841895, -279667074, 675176043, -163001916, 3935214363,  

Identity: 2lesfor(pos)seq + 2lesfor(neg)seq =  2lesforseq

We have 2lesforseq = 3*A000129(n+1);  2lesfor(pos)seq(2n) = A001541(n+1)
;
2lesfor(pos)seq(2n+1) = A001653(n) ; 2lesfor(neg)seq(2n) = A001542(n) ;
2lesfor(neg)seq(2n+1) = A002315(n)

-  http://www.research.att.com/projects/OEIS?Anum=A002315 
NSW numbers

-  http://www.research.att.com/projects/OEIS?Anum=A001542
A001542 = A000129(2n) 

-  http://www.research.att.com/projects/OEIS?Anum=A001653
 2*n^2 - 1 is a square.

-  http://www.research.att.com/projects/OEIS?Anum=A001541
Chebyshev polynomials of the first kind evaluated at 3.

-  http://www.research.att.com/projects/OEIS?Anum=A000129
Pell numbers

In my opinion, submitting several of the above relations as individual
comments will make it hard for future readers to see that the
information was actually generated "at once". Any suggestions on how to
submit this best as a comment?

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)