|
%I #22 Sep 16 2023 06:49:51
%S 1,3,81,19683,43046721,847288609443,150094635296999121,
%T 239299329230617529590083,3433683820292512484657849089281,
%U 443426488243037769948249630619149892803
%N a(n) = 3^(n^2).
%C The number of n X n {-1,0,1}-matrices (the same as the number of n X n matrices over GF(3) ).
%H Harry J. Smith, <a href="/A060722/b060722.txt">Table of n, a(n) for n=0,...,45</a>
%H Robert Corless and Steven Thornton, <a href="http://www.bohemianmatrices.com/assets/images/posters/The_Bohemian_Eigenvalue_Project-FIRS_2017.pdf">The Bohemian Eigenvalue Project</a>, 2017 poster.
%H Joël Gay and Vincent Pilaud, <a href="https://arxiv.org/abs/1804.06572">The weak order on Weyl posets</a>, arXiv:1804.06572 [math.CO], 2018.
%F a(n) = [x^n] 1/(1 - 3^n*x). - _Ilya Gutkovskiy_, Oct 10 2017
%p for n from 1 to 15 do printf(`%d,`,3^(n^2)) od:
%t Array[3^(#^2) &, 9] (* _Michael De Vlieger_, Jul 12 2018 *)
%o (PARI) { for (n=0, 45, write("b060722.txt", n, " ", 3^(n^2)); ) } \\ _Harry J. Smith_, Jul 10 2009
%o (PARI) a(n) = 3^(n^2); \\ _Joerg Arndt_, Feb 23 2014
%K nonn,easy
%O 0,2
%A Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
%E More terms from _James A. Sellers_, Apr 24 2001
%E a(0) = 1 added by _N. J. A. Sloane_, Nov 23 2007
| 