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A202637
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x-values in the solution to x^2 - 7*y^2 = -3.
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2
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2, 5, 37, 82, 590, 1307, 9403, 20830, 149858, 331973, 2388325, 5290738, 38063342, 84319835, 606625147, 1343826622, 9667939010, 21416906117, 154080399013, 341326671250, 2455618445198, 5439809833883, 39135814724155, 86695630670878
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OFFSET
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1,1
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COMMENTS
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The corresponding values of y of this Pell equation are in A202638.
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LINKS
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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).
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FORMULA
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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).
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MATHEMATICA
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LinearRecurrence[{0, 16, 0, -1}, {2, 5, 37, 82}, 24]
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PROG
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(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);
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CROSSREFS
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Sequence in context: A106129 A163499 A086218 * A138658 A067464 A081545
Adjacent sequences: A202634 A202635 A202636 * A202638 A202639 A202640
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Dec 22 2011
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STATUS
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approved
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