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A156853
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a(n) = 2025*n^2 - 649*n + 52.
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4
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1428, 6854, 16330, 29856, 47432, 69058, 94734, 124460, 158236, 196062, 237938, 283864, 333840, 387866, 445942, 508068, 574244, 644470, 718746, 797072, 879448, 965874, 1056350, 1150876, 1249452, 1352078, 1458754, 1569480, 1684256
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OFFSET
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1,1
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COMMENTS
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The identity (32805000*n^2 - 55096200*n + 23133601)^2 - (2025*n^2 - 649*n + 52)*(729000*n - 612180)^2 = 1 can be written as A157078(n)^2 - a(n)*A156865(n)^2 = 1.
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(1428 + 2570*x + 52*x^2)/(1-x)^3.
E.g.f.: -52 + (52 + 1376*x + 2025*x^2)*exp(x). - G. C. Greubel, Jan 27 2022
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1428, 6854, 16330}, 40]
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PROG
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(Magma) I:=[1428, 6854, 16330]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(Sage) [(25*n -4)*(81*n -13) for n in (1..30)] # G. C. Greubel, Jan 27 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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