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A157431
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a(n) = 4*n^2 + 73*n + 333.
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3
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410, 495, 588, 689, 798, 915, 1040, 1173, 1314, 1463, 1620, 1785, 1958, 2139, 2328, 2525, 2730, 2943, 3164, 3393, 3630, 3875, 4128, 4389, 4658, 4935, 5220, 5513, 5814, 6123, 6440, 6765, 7098, 7439, 7788, 8145, 8510, 8883, 9264, 9653, 10050, 10455
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OFFSET
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1,1
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COMMENTS
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The identity (128*n^2+2336*n+10657)^2-(4*n^2+73*n+333)*( (64*n+584)^2=1 can be written as A157433(n)^2-a(n)*A157432(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.: -(264*x^2-589*x+333)/(x-1)^3. [corrected by Georg Fischer, May 12 2019]
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {410, 495, 588}, 50]
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PROG
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(Magma) I:=[410, 495, 588]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 4*n^2 + 73*n + 333.
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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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