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A157378
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a(n) = 43046721*n^2 - 50729652*n + 14945957.
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3
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7263026, 85673537, 250177490, 500774885, 837465722, 1260250001, 1769127722, 2364098885, 3045163490, 3812321537, 4665573026, 5604917957, 6630356330, 7741888145, 8939513402, 10223232101, 11593044242, 13048949825, 14590948850, 16219041317
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OFFSET
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1,1
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COMMENTS
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The identity (43046721*n^2 - 50729652*n + 14945959)^2 - (6561*n^2 - 7732*n + 2278)*(531441*n - 313146)^2 = 1 can be written as a(n)^2 - A157376(n)*A157377(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*(7263026 + 63884459*x + 14945957*x^2)/(1-x)^3.
E.g.f.: (6561*x*(6561*x - 1171) + 14945957)*exp(x) - 14945957. - G. C. Greubel, Feb 04 2018
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {7263026, 85673537, 250177490}, 40]
Table[43046721*n^2 - 50729652*n + 14945957, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)
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PROG
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(Magma) I:=[7263026, 85673537, 250177490]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(PARI) a(n) = 43046721*n^2 - 50729652*n + 14945957.
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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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