A202638 y-values in the solution to x^2 - 7*y^2 = -3.

1, 2, 14, 31, 223, 494, 3554, 7873, 56641, 125474, 902702, 1999711, 14386591, 31869902, 229282754, 507918721, 3654137473, 8094829634, 58236916814, 129009355423, 928136531551, 2056054857134, 14791947588002, 32767868358721

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A202637.

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

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).

Index entries for linear recurrences with constant coefficients, signature (0,16,0,-1).

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

Adjacent sequences: A202635 A202636 A202637 * A202639 A202640 A202641

Keyword

nonn,easy

Author

Bruno Berselli, Dec 22 2011

Status

approved