OFFSET
0,3
COMMENTS
a(n) is the number of maximal chains in the lattice of subspaces of an n-dimensional vector space over GF(3). - Geoffrey Critzer, Sep 07 2022
LINKS
FORMULA
a(n) = Product_{k=1..n} (q^k - 1) / (q - 1).
a(0) = 1, a(n) = (3^n - 1)*a(n-1)/2. - Vincenzo Librandi, Oct 27 2012
a(n) = (Product_{i=0..n-1} (q^n-q^i))/((q-1)^n*q^binomial(n,2)) = A053290(n)/(A000079(n)*A047656(n)). - Geoffrey Critzer, Sep 07 2022
MATHEMATICA
RecurrenceTable[{a[1]==1, a[n]==((3^n - 1) * a[n-1])/2}, a, {n, 15}] (* Vincenzo Librandi, Oct 27 2012 *)
Table[QFactorial[n, 3], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)
PROG
(Magma) [n le 1 select 1 else (3^n-1)*Self(n-1)/2: n in [1..15]]; // Vincenzo Librandi, Oct 22 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Sep 08 2021
STATUS
approved