OFFSET
2,1
COMMENTS
In the reference a more general formula is given for the number of such matrices over GF(q) for any q.
LINKS
Robert Israel, Table of n, a(n) for n = 2..113
Shalosh B. Ekhad, Doron Zeilberger, An Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Field, arXiv:math/9512224 [math.CO], 1995.
Shalosh B. Ekhad, Doron Zeilberger, An Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Field, Elec. J. Comb. 3(1)(1996).
FORMULA
a(2n) = Sum_{j>=0} (C(2n, n - 3j) - C(2n, n - 3j - 1)) * 2^(n^2 - 3j^2 - j).
a(2n+1) = Sum_{j>=0} (C(2n + 1, n - 3j) - C(2n + 1, n - 3j - 1)) * 2^(n^2 + n - 3j^2 - 2j)
MAPLE
feven:= n -> add((binomial(2*n, n-3*j) - binomial(2*n, n-3*j-1))*2^(n^2-3*j^2-j), j=0..n/3):
fodd:= n -> add((binomial(2*n+1, n-3*j)-binomial(2*n+1, n-3*j-1))*2^(n^2+n-3*j^2-2*j), j=0..n/3):
seq(op([feven(i), fodd(i)]), i=1..20); # Robert Israel, Mar 01 2017
MATHEMATICA
a[n_] := Sum[If[EvenQ[n], (Binomial[n, n/2 - 3j] - Binomial[n, n/2 - 3j - 1])*2^((n/2)^2 - 3j^2 - j), (Binomial[n, (n-1)/2 - 3j] - Binomial[n, (n-1)/2 - 3j - 1])*2^(((n-1)/2)^2 + (n-1)/2 - 3j^2 - 2j)], {j, 0, n/3}];
Table[a[n], {n, 2, 20}] (* Jean-François Alcover, Sep 18 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 30 2001
EXTENSIONS
More terms from Vladeta Jovovic, Aug 01 2001
Edited and more terms added by Robert Israel, Mar 01 2017
STATUS
approved