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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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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.
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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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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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