[seqfan] the comments

[vincenzo.librandi at tin.it]

Dear, All, the comments:

%C A001105 Except the first term, numbers n 
such that (9*n^3)/8 is a
square. Example: (9*2^3)/8=9=3^2; (9*8^3)
/8=576=24^2;
(9*18^3)/8=6561=81^2; (9*32^3)/8=36864=192^2; [From 
Vincenzo Librandi
(vincenzo.librandi(AT)tin.it), Feb 16 2009]

%C 
A001081 Except the first term of [A001080] and of [A001081], If
X=
[A001081] (1,8,127,2024,32257,..,); Y=[A001080]
(0,3,48,765,1192,..,) 
and A=[A010727] (7,7,7,..,) we have, for all
terms, Pell's equation X^2-
A*Y^2=1. Example: 8^2-7*3^2=1;
127^2-7*48^2=1; 2024^2-7*765^2=1; 
32257^2-7*12192^2=1; [From Vincenzo
Librandi (vincenzo.librandi(AT)tin.
it), Feb 16 2009]
%Y A001081 Cf. A001080, A010727 [From Vincenzo 
Librandi
(vincenzo.librandi(AT)tin.it), Feb 16 2009]

%F A011944 a(n)
=14*a(n-1)-a(n-2), with a(1)=0, a(2)=2: Example:
a(3)=14*a(2)-a(1)=14*2-
0=28; a(4)=14*28-2=390; a(5)=14*390-28=5432.
[From Vincenzo Librandi 
(vincenzo.librandi(AT)tin.it), Feb 16 2009]

%C A010727 Except the 
first term of [A001080] and of [A001081], If
X=[A001081] 
(1,8,127,2024,32257,..,); Y=[A001080]
(0,3,48,765,1192,..,) and A=
[A010727] (7,7,7,..,) we have, for all
terms, Pell's equation X^2-
A*Y^2=1. Example: 8^2-7*3^2=1;
127^2-7*48^2=1; 2024^2-7*765^2=1; 
32257^2-7*12192^2=1; [From Vincenzo
Librandi (vincenzo.librandi(AT)tin.
it), Feb 16 2009]
%Y A010727 Cf. A001080, A001081 [From Vincenzo 
Librandi
(vincenzo.librandi(AT)tin.it), Feb 16 2009]

%C A001080 Except 
the first term of [A001080] and of [A001081], If
X=[A001081] 
(1,8,127,2024,32257,..,); Y=[A001080]
(0,3,48,765,1192,..,) and A=
[A010727] (7,7,7,..,) we have, for all
terms, Pell's equation X^2-
A*Y^2=1. Example: 8^2-7*3^2=1;
127^2-7*48^2=1; 2024^2-7*765^2=1; 
32257^2-7*12192^2=1; [From Vincenzo
Librandi (vincenzo.librandi(AT)tin.
it), Feb 16 2009]
%Y A001080 Cf. A001081, A010727 [From Vincenzo 
Librandi
(vincenzo.librandi(AT)tin.it), Feb 16 2009]

%C A047522 Except 
for the first term of [A047522] ad the first term of
[A074378], if X=
[A047522], Y=[A010709], A=[A074378], we have, for all
other terms, 
Pell's equation X^2-A*Y^2=1. Example 9^2-5*4^2=1;
15^2-14*4^2=1; 17^2-
18*4^2=1 [From Vincenzo Librandi
(vincenzo.librandi(AT)tin.it), Feb 14 
2009]
%Y A047522 Cf. A010709, A074378 [From Vincenzo Librandi
(vincenzo.
librandi(AT)tin.it), Feb 14 2009]

 %C A078371 Except the two terms of 
[A141530] ad the first term of
[A046092[, if X=[A141530], A=[A078371], 
Y=[A046092], we have, for all
others terms, Pell's equation: X^2-
A*Y^2=1. Example: 9^2-5*4^2=1;
55^2-21*12^2=1; 161^2-45*24^2=1. [From 
Vincenzo Librandi
(vincenzo.librandi(AT)tin.it), Feb 13 2009]
%Y 
A078371 Cf. A046092, A141530 [From Vincenzo Librandi
(vincenzo.librandi
(AT)tin.it), Feb 13 2009]
 

%C A046092 Except the two terms of 
[A141530] ad the first term of
[A046092[, if X=[A141530], A=[A078371], 
Y=[A046092], we have, for all
others terms, Pell's equation: X^2-
A*Y^2=1. Example: 9^2-5*4^2=1;
55^2-21*12^2=1; 161^2-45*24^2=1. [From 
Vincenzo Librandi
(vincenzo.librandi(AT)tin.it), Feb 13 2009]
%Y 
A046092 Cf. A078371, A141530 [From Vincenzo Librandi
(vincenzo.librandi
(AT)tin.it), Feb 13 2009]


Regards, 
Vincenzo Librandi