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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

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Last modified December 4 19:34 EST 2023. Contains 367563 sequences. (Running on oeis4.)