A060722 a(n) = 3^(n^2).

1, 3, 81, 19683, 43046721, 847288609443, 150094635296999121, 239299329230617529590083, 3433683820292512484657849089281, 443426488243037769948249630619149892803

Offset: 0

Author

Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001

Keywords

• nonn
• easy

Comments

The number of n X n {-1,0,1}-matrices (the same as the number of n X n matrices over GF(3) ).

Links

• Harry J. Smith, Table of n, a(n) for n = 0..45
• Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster.
• Joël Gay and Vincent Pilaud, The weak order on Weyl posets, arXiv:1804.06572 [math.CO], 2018.

Crossrefs

Cf. A053290, A053764, A378666.

Programs

Maple

for n from 1 to 15 do printf(`%d,`,3^(n^2)) od:

Mathematica

Array[3^(#^2) &, 9] (* Michael De Vlieger, Jul 12 2018 *)

PARI

{ for (n=0, 45, write("b060722.txt", n, " ", 3^(n^2)); ) } \\ Harry J. Smith, Jul 10 2009

PARI

a(n) = 3^(n^2); \\ Joerg Arndt, Feb 23 2014

Formula

a(n) = [x^n] 1/(1 - 3^n*x). - Ilya Gutkovskiy, Oct 10 2017

From Geoffrey Critzer, Dec 02 2024: (Start)

a(n) = Sum_{k=0..n} A378666(n,k)*A053764(k)*A053290(n-k).

Sum_{n>=0} a(n)x^n/B(n) = f(x)*g(x) where f(x) = Sum_{n>=0} A053290(n)x^n/B(n) and g(x) = Sum_{n>=0} A053764(n)x^n/B(n) and B(n) = A053290(n)/2^n. (End)

Extensions

More terms from James Sellers, Apr 24 2001

a(0) = 1 added by N. J. A. Sloane, Nov 23 2007