OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..721 (first 51 terms from Vincenzo Librandi)
FORMULA
G.f.: Sum_{n>=0} (1+x)^n*(1+x^2)^binomial(n,2)/2^(n+1).
G.f.: Sum_{n>=0} (Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*(1+x)^k*(1+x^2)^binomial(k,2)).
EXAMPLE
From Gus Wiseman, Nov 14 2018: (Start)
The a(4) = 20 matrices:
[11]
[11]
.
[110][101][100][100][011][010][010][001][001]
[100][010][011][001][100][110][101][010][001]
[001][100][010][011][100][001][010][101][110]
.
[1000][1000][1000][1000][0100][0100][0010][0010][0001][0001]
[0100][0100][0010][0001][1000][1000][0100][0001][0100][0010]
[0010][0001][0100][0010][0010][0001][1000][1000][0010][0100]
[0001][0010][0001][0100][0001][0010][0001][0100][1000][1000]
(End)
MATHEMATICA
Table[Sum[SeriesCoefficient[(1+x)^k*(1+x^2)^(k*(k-1)/2)/2^(k+1), {x, 0, n}], {k, 0, Infinity}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 02 2014 *)
Join[{1}, Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], Sort[Reverse/@#]==#]&]], {n, 5}]] (* Gus Wiseman, Nov 14 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 25 2008, Mar 03 2008, Mar 04 2008
STATUS
approved