[seqfan] Re: A077057 and A077058

[wl at particle.uni-karlsruhe.de]

Dear seqfans,

in A077057 the values for n = 9, 33 and 54 should, according to my 
online-program

http://www-itp.particle.uni-karlsruhe.de/~wl/BinQuadForm.html

be  a(9) = 4, a(33) = 2353, a(54) = 25.

These values appear for  G = A078358:  G(9) = 11, G(33) = 38, G(54) = 61
and the companion values A077058 are correct: 1, 352, 3, respectively.
All three cases are for the +1 case of x^2 - x*y - G y^2 = +1 or -1. 
There are no solutions for the -1 case.

4^2 - 4*1 - 11*1^2 = +1
2353^2  - 2353*352 - 38*352^2 = +1
25^2 - 25*3 - 61*3^2 = +1

I am to blame for the typo for A077057(9). In fact, I (tried to)gave 
Perron's table p. 108 (the first 28 entries of x and y) and Perron has 
for G=11 indeed 4 (not my 3).
I am very sorry about this and I will correct this, when I have checked 
also the other values.
Thanks to Jean-François Alcover  and Susanne Wienand.
Regards,
Wolfdieter Lang