login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202637 x-values in the solution to x^2 - 7*y^2 = -3. 2
2, 5, 37, 82, 590, 1307, 9403, 20830, 149858, 331973, 2388325, 5290738, 38063342, 84319835, 606625147, 1343826622, 9667939010, 21416906117, 154080399013, 341326671250, 2455618445198, 5439809833883, 39135814724155, 86695630670878 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The corresponding values of y of this Pell equation are in A202638.
LINKS
R. A. Mollin, Class Numbers of Quadratic Fields Determinet by Solvability of Diophantine Equations, Mathematics of Computation Vol. 48, 1987, p. 235 (Theorem 1.1, particular case).
FORMULA
G.f.: x*(1+x)*(2+3*x+2*x^2)/(1-16*x^2+x^4).
a(n) = -a(-n+1) = ((-2*(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-(2*(-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2.
a(2n)-a(2n-1) = A202638(2n)+A202638(2n-1).
MATHEMATICA
LinearRecurrence[{0, 16, 0, -1}, {2, 5, 37, 82}, 24]
PROG
(PARI) a=vector(24); a[1]=2; a[2]=5; a[3]=37; a[4]=82; for(i=5, #a, a[i]=16*a[i-2]-a[i-4]); a
(Magma) m:=24; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)*(2+3*x+2*x^2)/(1-16*x^2+x^4)));
(Maxima) makelist(expand(((-2*(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-(2*(-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2), n, 1, 24);
CROSSREFS
Sequence in context: A106129 A163499 A086218 * A138658 A067464 A081545
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 22 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 12:09 EDT 2024. Contains 374318 sequences. (Running on oeis4.)