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0, 3, 24, 81, 192, 375, 648, 1029, 1536, 2187, 3000, 3993, 5184, 6591, 8232, 10125, 12288, 14739, 17496, 20577, 24000, 27783, 31944, 36501, 41472, 46875, 52728, 59049, 65856, 73167, 81000, 89373, 98304, 107811, 117912, 128625, 139968, 151959, 164616
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OFFSET
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0,2
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COMMENTS
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a(n)^2 = (2n^2)^3 + n^6, thus (A001105(n), A001447(n), a(n)) (n > 0) is a solution of the Diophantine equation x^3 + y^6 = z^2. - XU Pingya, Oct 11 2017
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n+1) = a(n) + 9*n^2 + 9*n + 3 with a(0) = 0. - Jean-Bernard François, Oct 04 2013
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, May 27 2021
From Amiram Eldar, Jan 10 2023: (Start)
Sum_{n>=1} 1/a(n) = zeta(3)/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = zeta(3)/4. (End)
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MAPLE
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seq(3*n^3, n=0..38); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
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3Range[0, 35]^3 (* Alonso del Arte, Oct 04 2013 *)
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PROG
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(Magma) [3*n^3: n in [0..40]]; // Vincenzo Librandi, Jun 26 2011
(PARI) a(n)=3*n^3 \\ Charles R Greathouse IV, Oct 12 2017
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CROSSREFS
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Cf. A000578, A001105, A001447, A002117, A033431.
Sequence in context: A347108 A027158 A251781 * A220834 A276243 A211618
Adjacent sequences: A117639 A117640 A117641 * A117643 A117644 A117645
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, Apr 10 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, Apr 30 2006
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STATUS
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approved
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