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A262666
Irregular table read by rows: T(n,k) is the number of binary bisymmetric n X n matrices with exactly k 1's; n>=0, 0<=k<=n^2.
4
1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 4, 0, 8, 0, 12, 0, 14, 0, 12, 0, 8, 0, 4, 0, 1, 1, 1, 4, 4, 10, 10, 20, 20, 31, 31, 40, 40, 44, 44, 40, 40, 31, 31, 20, 20, 10, 10, 4, 4, 1, 1, 1, 0, 6, 0, 21, 0, 56, 0, 120, 0, 216, 0, 336, 0, 456, 0
OFFSET
0,6
COMMENTS
T(n,k) = 0 if n is even and k is odd.
T(n,k) = T(n,k+1) if n is odd and k is even.
LINKS
FORMULA
G.f. for row n: (1+x)^t*(1+x^2)^(n-t)*(1+x^4)^(((n-2)*n+t)/4) where t = n mod 2. - Alois P. Heinz, Sep 27 2015
EXAMPLE
Irregular table begins:
n\k 0 1 2 3 4 5 6 7 8 9 ...
0: 1
1: 1 1
2: 1 0 2 0 1
3: 1 1 2 2 2 2 2 2 1 1
4: 1 0 4 0 8 0 12 0 14 0 ...
5: 1 1 4 4 10 10 20 20 31 31 ...
...
MAPLE
T:= n-> seq(coeff((t->(1+x^2)^(n-t)*(1+x)^t*(1+x^4)^
(((n-2)*n+t)/4))(irem(n, 2)), x, i), i=0..n^2):
seq(T(n), n=0..6); # Alois P. Heinz, Sep 27 2015
CROSSREFS
Row sums give A060656(n+1).
Columns k=0-3 give: A000012, A000035, A052928, A237420(n+1).
Sequence in context: A349465 A035697 A135549 * A124737 A121303 A166396
KEYWORD
nonn,tabf
AUTHOR
Kival Ngaokrajang, Sep 26 2015
EXTENSIONS
More terms from Alois P. Heinz, Sep 27 2015
STATUS
approved