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A202638 y-values in the solution to x^2 - 7*y^2 = -3. 2
1, 2, 14, 31, 223, 494, 3554, 7873, 56641, 125474, 902702, 1999711, 14386591, 31869902, 229282754, 507918721, 3654137473, 8094829634, 58236916814, 129009355423, 928136531551, 2056054857134, 14791947588002, 32767868358721 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The corresponding values of x of this Pell equation are in A202637.
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)*(1+3*x+x^2)/(1-16*x^2+x^4).
a(n) = a(-n+1) = ((7+2*sqrt(7)*(-1)^n)*(8-3*sqrt(7))^floor(n/2)+(7-2*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^floor(n/2))/14.
a(2n)+a(2n-1) = A202637(2n)-A202637(2n-1).
MATHEMATICA
LinearRecurrence[{0, 16, 0, -1}, {1, 2, 14, 31}, 24]
PROG
(PARI) a=vector(24); a[1]=1; a[2]=2; a[3]=14; a[4]=31; 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)*(1+3*x+x^2)/(1-16*x^2+x^4)));
(Maxima) makelist(expand(((7+2*sqrt(7)*(-1)^n)*(8-3*sqrt(7))^floor(n/2)+(7-2*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^floor(n/2))/14), n, 1, 24);
CROSSREFS
Sequence in context: A031301 A335200 A294558 * A226565 A231050 A337338
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 22 2011
STATUS
approved

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Last modified June 19 11:49 EDT 2024. Contains 373503 sequences. (Running on oeis4.)