A017162 a(n) = (9*n)^2.

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, 77841, 82944, 88209, 93636, 99225, 104976, 110889, 116964, 123201

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

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)

From Elmo R. Oliveira, Dec 02 2024: (Start)

E.g.f.: 81*exp(x)*x*(1 + x).

a(n) = 81*A000290(n) = A008591(n)^2 = A000290(A008591(n)). (End)

Mathematica

(9*Range[0, 30])^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 81, 324}, 40] (* Harvey P. Dale, Nov 06 2012 *)

Prog

(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

Crossrefs

Cf. A000290, A008591.

Sequence in context: A237412 A237405 A250443 * A250427 A236828 A236821

Adjacent sequences: A017159 A017160 A017161 * A017163 A017164 A017165

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved