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A370059
Number of traceless symmetric binary matrices with 2n 1's and all row sums >= 2.
2
1, 0, 0, 1, 3, 18, 156, 1555, 17907, 234031, 3414375, 54984258, 968680368, 18532158756, 382616109012, 8479409847277, 200776196593073, 5058600736907013, 135130222251100358, 3814891312969572209, 113492694557655580989, 3548800852807887882157, 116359373033373284971070
OFFSET
0,5
LINKS
EXAMPLE
The a(3) = 1 matrix is:
[0 1 1]
[1 0 1]
[1 1 0]
The a(4) = 3 matrices are:
[0 0 1 1] [0 1 0 1] [0 1 1 0]
[0 0 1 1] [1 0 1 0] [1 0 0 1]
[1 1 0 0] [0 1 0 1] [1 0 0 1]
[1 1 0 0] [1 0 1 0] [0 1 1 0]
PROG
(PARI) G(n)={my(A=x/exp(x*y + O(x*x^n))); exp(y*x^2/2 - x + O(x*x^n)) * sum(k=0, n, (1 + y + O(y*y^n))^binomial(k, 2)*A^k/k!)}
seq(n)={Vec(subst(Pol(serlaplace(G(n))), x, 1))}
CROSSREFS
Row sums of A369931.
Cf. A001205 (row sums of matrices exactly 2).
Sequence in context: A145350 A107888 A293491 * A138274 A375945 A375877
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 08 2024
STATUS
approved