OFFSET
0,2
COMMENTS
This sequence is computed with g(1e9,21) in the PARI program.
A Pellian equation - Benoit Cloitre, Feb 03 2006
Numbers m such that 21*(m^2-1) is square. - Vincenzo Librandi, Nov 13 2010
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..489 (terms 0..130 from Vincenzo Librandi)
Tanya Khovanova, Recursive Sequences
John Robertson, Home page.
Index entries for linear recurrences with constant coefficients, signature (110, -1).
FORMULA
a(0)=1, a(1)=55, a(n)=110*a(n-1)-a(n-2). - Benoit Cloitre, Feb 03 2006
G.f.: (1-55*x)/(1-110*x+x^2). - Philippe Deléham, Nov 18 2008
EXAMPLE
(55^2-1)/21 = 12^2
MATHEMATICA
Table[ Numerator@ FromContinuedFraction@ ContinuedFraction[Sqrt@21, Length@ Last@ ContinuedFraction@ Sqrt@21*n], {n, 12}] (* Robert G. Wilson v, Feb 28 2006 *)
LinearRecurrence[{110, -1}, {1, 55}, 20] (* Harvey P. Dale, Jan 27 2013 *)
PROG
(PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))
(PARI) a0=1; a1=55; for(n=2, 30, a2=110*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 01 2006
EXTENSIONS
More terms from Benoit Cloitre, Feb 03 2006
STATUS
approved