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A157842
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a(n) = 3600*n^2 - 5599*n + 2177.
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3
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178, 5379, 17780, 37381, 64182, 98183, 139384, 187785, 243386, 306187, 376188, 453389, 537790, 629391, 728192, 834193, 947394, 1067795, 1195396, 1330197, 1472198, 1621399, 1777800, 1941401, 2112202, 2290203, 2475404, 2667805
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OFFSET
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1,1
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COMMENTS
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The identity (103680000*n^2-161251200*n+62697601)^2-(3600*n^2-5599*n+2177)*(1728000*n-1343760)^2=1 can be written as A157844(n)^2-a(n)*A157843(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*(-178-4845*x-2177*x^2)/(x-1)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {178, 5379, 17780}, 40]
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PROG
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(Magma) I:=[178, 5379, 17780]; [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) = 3600*n^2 - 5599*n + 2177.
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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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