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A017162
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a(n) = (9*n)^2.
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4
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0, 81, 324, 729, 1296, 2025, 2916, 3969, 5184, 6561, 8100, 9801, 11664, 13689, 15876, 18225, 20736, 23409, 26244, 29241, 32400, 35721, 39204, 42849, 46656, 50625, 54756, 59049, 63504, 68121, 72900
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OFFSET
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0,2
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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 (3,-3,1).
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=81, a(2)=324. - Harvey P. Dale, Nov 06 2012
G.f.: -81*x*(1+x) / (x-1)^3. - R. J. Mathar, Jul 17 2014
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/486.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/972.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/9)/(Pi/9).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/9)/(Pi/9). (End)
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MATHEMATICA
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(9*Range[0, 30])^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 81, 324}, 40] (* Harvey P. Dale, Nov 06 2012 *)
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PROG
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(Magma) [(9*n)^2: n in [0..35]]; // Vincenzo Librandi, Jul 22 2011
(PARI) a(n)=(9*n)^2 \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Sequence in context: A237412 A237405 A250443 * A250427 A236828 A236821
Adjacent sequences: A017159 A017160 A017161 * A017163 A017164 A017165
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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