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A174772
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y-values in the solution to x^2 - 33*y^2 = 1.
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2
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0, 4, 184, 8460, 388976, 17884436, 822295080, 37807689244, 1738331410144, 79925437177380, 3674831778749336, 168962336385292076, 7768592641944686160, 357186299193070271284, 16422801170239287792904, 755091667531814168202300, 34717793905293212449512896
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OFFSET
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1,2
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COMMENTS
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The corresponding values of x of this Pell equation are in A174748.
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LINKS
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FORMULA
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a(n) = 46*a(n-1)-a(n-2) with a(1)=0, a(2)=4.
G.f.: 4*x^2/(1-46*x+x^2).
a(n) = 4*S(n-2,46), n>=1, with Chebyshev's S polynomials A049310 and S(-1,x)=0. - Wolfdieter Lang, Jun 19 2013
a(n) = (-4+23/sqrt(33))*(23+4*sqrt(33))^(-n)*(-1057-184*sqrt(33)+(23+4*sqrt(33))^(2*n))/2. - Colin Barker, Jun 10 2016
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EXAMPLE
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For n=3 a(3)=46*4-0=184; n=4, a(4)=46*184-4=8460.
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MATHEMATICA
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LinearRecurrence[{46, -1}, {0, 4}, 30]
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PROG
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(Magma) I:=[0, 4]; [n le 2 select I[n] else 46*Self(n-1)-Self(n-2): n in [1..20]];
(PARI) Vec(4*x^2/(1-46*x+x^2) + O(x^20)) \\ Colin Barker, Jun 10 2016
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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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