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A157105
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a(n) = 137842*n - 30996.
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4
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106846, 244688, 382530, 520372, 658214, 796056, 933898, 1071740, 1209582, 1347424, 1485266, 1623108, 1760950, 1898792, 2036634, 2174476, 2312318, 2450160, 2588002, 2725844, 2863686, 3001528, 3139370, 3277212, 3415054
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OFFSET
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1,1
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COMMENTS
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The identity (5651522*n^2 - 2541672*n + 285769)^2 - (1681*n^2 - 756*n + 85)*(137842*n - 30996)^2 = 1 can be written as (A157106(n))^2 - (A157010(n))*(a(n))^2 = 1.
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LINKS
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FORMULA
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a(n) = 2*a(n-1) -a(n-2).
G.f: 82*x*(1303 + 378*x)/(1-x)^2.
E.g.f.: 82*(378 - (378 - 1681*x)*exp(x)). - G. C. Greubel, Jan 11 2022
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MATHEMATICA
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LinearRecurrence[{2, -1}, {106846, 244688}, 30] (* Harvey P. Dale, Mar 31 2013 *)
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PROG
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(Magma) I:=[106846, 244688, 382530]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 137842*n - 30996
(Sage) [82*(1681*n - 378) for n in (1..30)] # G. C. Greubel, Jan 11 2022
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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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