login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A017162
a(n) = (9*n)^2.
3
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
OFFSET
0,2
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)
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
Sequence in context: A237412 A237405 A250443 * A250427 A236828 A236821
KEYWORD
nonn,easy
STATUS
approved