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A017522
a(n) = (12*n)^2.
3
0, 144, 576, 1296, 2304, 3600, 5184, 7056, 9216, 11664, 14400, 17424, 20736, 24336, 28224, 32400, 36864, 41616, 46656, 51984, 57600, 63504, 69696, 76176, 82944, 90000, 97344, 104976, 112896, 121104
OFFSET
0,2
FORMULA
G.f.: 144*x*(1+x)/(1-x)^3. - Bruno Berselli, Feb 10 2012
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/864.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1728.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/12)/(Pi/12).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/12)/(Pi/12) = 3*sqrt(2)*(sqrt(3)-1)/Pi. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {0, 144, 576}, 50] (* Vincenzo Librandi, Feb 10 2012 *)
(12 Range[0, 30])^2 (* Bruno Berselli, Feb 10 2012 *)
PROG
(Magma) [(12*n)^2: n in [0..35]]; // Vincenzo Librandi, Feb 10 2012
(PARI) a(n)=(12*n)^2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A000290 (n^2), A008594 (12*n).
Sequence in context: A262797 A017402 A155707 * A180413 A137885 A204398
KEYWORD
nonn,easy
STATUS
approved