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Number of unlabeled simple graphs with n edges rooted at two indistinguishable vertices.

4

`%I #5 Nov 22 2020 12:21:54
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`%S 1,3,9,28,87,276,909,3086,10879,39821,151363,597062,2442044,10342904,
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`%T 45301072,204895366,955661003,4590214994,22675644514,115068710553,
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`%U 599149303234,3197694533771,17475917252052,97712883807625,558481251055893,3260409769087068
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`%N Number of unlabeled simple graphs with n edges rooted at two indistinguishable vertices.
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`%e The a(1) = 3 cases correspond to a single edge which can be attached to zero, one or both of the roots.
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`%o (PARI) \\ See A339063 for G.
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`%o seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/2)}
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`%Y Cf. A000664, A053419 (one root), A303829, A339041, A339063, A339065.
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`%K nonn
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`%O 0,2
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`%A _Andrew Howroyd_, Nov 22 2020
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