OFFSET
0,2
COMMENTS
Number of upper triangular 3 X 3 {0,1,...,n}-matrices with no zero rows or columns.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = n^3*(n+1)*(n^2+3*n+1) = n^6 + 4*n^5 + 4*n^4 + n^3.
G.f.: 2*x*(4*x^4-55*x^3-207*x^2-97*x-5)/(x-1)^7.
EXAMPLE
a(1) = 10:
[100] [110] [100] [110] [101] [111] [101] [111] [110] [111]
[ 10] [ 10] [ 11] [ 11] [ 10] [ 10] [ 11] [ 11] [ 01] [ 01]
[ 1] [ 1] [ 1] [ 1] [ 1] [ 1] [ 1] [ 1] [ 1] [ 1].
MAPLE
a:= n-> n^3*(n+1)*(n^2+3*n+1):
seq(a(n), n=0..28);
MATHEMATICA
Table[n^3*(n + 1)*(n^2 + 3*n + 1), {n, 0, 50}] (* Paolo Xausa, Jun 09 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jan 23 2024
STATUS
approved