Relation between A011944 and A005246, A002531

[Rainer Rosenthal]

Dear SeqFan,

solving a problem in de.rec.denksport yesterday
(Problem #743 by Gerhard Woeginger) I was urged
to find solutions where 12*t+1 had to be a square
while t itself must be square.

In short: I did have to solve  w^2 = (12*h^2 + 1)
in natural numbers w and h. I will write w = w(h)
in the tables below.

Searching the OEIS I did find the h-sequence:
A011944 a(n) = 14a(n-1) - a(n-2) = 0, 2, 28, 390, ...
I will write h(n) in the tables below.

And looking for the w-sequence I did find two
sequences, which are closely related. 

A005246  A002531  Equal
      1        1   x
      1        1   x  = w(0) = w(h(0))
      1        2
      2        5
      3
      7        7   x  = w(2) = w(h(1))
     11       19
     26       26   x
     41       71
     97       97   x  = w(28) = w(h(2))
    153      165
    362      362   x
    571      989
   1351     1351   x  = w(390) = w(h(3))
   2131     3691
   5042     5042   x
   7953    13775
  18817    18817   x  = w(h(4))
  29681    51409
  70226    70226   x
 110771   191861
 262087   262087   x  = w(h(5))
 413403   716035
 978122   978122   x
1542841  2672279
3650401  3650401   x  = w(h(6))
-------------------------------------------
Table for comparing two sequences. 
Legend:  w(h) = sqrt(12 h^2 + 1)
         h = h(n) = A011944(n)

Once again I have been overwhelmed by the jewellerie
of the OEIS.
What sort of comment would you find appropriate for
my findings? A005246 and A002531 are already connected
by comments.

I would like to make a good comment - but I don't
trust my ability. No fishing for compliments and not
(only) lazyness!

Best regards,
Rainer Rosenthal
r.rosenthal at web.de