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A198949
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y-values in the solution to 11*x^2-10 = y^2.
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5
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1, 23, 43, 461, 859, 9197, 17137, 183479, 341881, 3660383, 6820483, 73024181, 136067779, 1456823237, 2714535097, 29063440559, 54154634161, 579811987943, 1080378148123, 11567176318301, 21553408328299, 230763714378077, 429987788417857, 4603707111243239
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OFFSET
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1,2
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COMMENTS
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When are both n+1 and 11*n+1 perfect squares? This problem gives the equation 11*x^2-10 = y^2.
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LINKS
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FORMULA
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a(n+4) = 20*a(n+2)-a(n) with a(1)=1, a(2)=23, a(3)=43, a(4)=461.
G.f.: x*(1+x)*(1+22*x+x^2)/(1-20*x^2+x^4). - Bruno Berselli, Nov 04 2011
a(n) = ((-(-1)^n-t)*(10-3*t)^floor(n/2)+(-(-1)^n+t)*(10+3*t)^floor(n/2))/2 where t=sqrt(11). - Bruno Berselli, Nov 14 2011
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MATHEMATICA
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LinearRecurrence[{0, 20, 0, -1}, {1, 23, 43, 461}, 24] (* Bruno Berselli, Nov 11 2011 *)
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PROG
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(Maxima) makelist(expand(((-(-1)^n-sqrt(11))*(10-3*sqrt(11))^floor(n/2)+(-(-1)^n+sqrt(11))*(10+3*sqrt(11))^floor(n/2))/2), n, 1, 24); /* Bruno Berselli, Nov 14 2011 */
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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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EXTENSIONS
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STATUS
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approved
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