A370059 Number of traceless symmetric binary matrices with 2n 1's and all row sums >= 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
Keywords
Examples
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]
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..200
Programs
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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))}