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A358248
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Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 8, up to isomorphism.
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7
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1, 10, 35, 99, 190, 332, 484, 680, 863, 1082, 1277, 1505, 1704, 1935, 2135, 2367, 2567, 2799, 2999, 3231, 3431, 3663, 3863, 4095, 4295, 4527, 4727, 4959, 5159, 5391, 5591, 5823, 6023, 6255, 6455, 6687, 6887, 7119, 7319, 7551, 7751, 7983, 8183, 8415, 8615, 8847
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OFFSET
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1,2
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COMMENTS
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Pseudographs are finite graphs with undirected edges without identity, where parallel edges between the same vertices and loops are allowed.
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LINKS
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EXAMPLE
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For n = 2 the a(2) = 10 such pseudographs are: 1. two vertices connected by a 8-edge and a 0-edge, 2. two vertices connected by a 7-edge and a 1-edge, 3. two vertices connected by a 6-edge and a 2-edge, 4. two vertices connected by a 5-edge and a 3-edge, 5. two vertices connected by two 4-edges, 6. two vertices where one has a 8-loop and the other one has a 0-loop, 7. two vertices where one has a 7-loop and the other one has a 1-loop, 8. two vertices where one has a 6-loop and the other one has a 2-loop, 9. two vertices where one has a 5-loop and the other one has a 3-loop, 10. two vertices with a 4-loop each.
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PROG
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(Julia)
using Combinatorics
function A(n::Int)
sum_total = 8
result = 0
for num_loops in 0:div(n, 2)
num_cross = n - 2 * num_loops
for sum_cross in 0:sum_total
for sum_loop1 in 0:sum_total-sum_cross
sum_loop2 = sum_total - sum_cross - sum_loop1
if sum_loop2 == sum_loop1
result +=
div(
npartitions_with_zero(sum_loop2, num_loops) *
(npartitions_with_zero(sum_loop2, num_loops) + 1),
2,
) * npartitions_with_zero(sum_cross, num_cross)
elseif sum_loop2 > sum_loop1
result +=
npartitions_with_zero(sum_loop2, num_loops) *
npartitions_with_zero(sum_loop1, num_loops) *
npartitions_with_zero(sum_cross, num_cross)
end
end
end
end
return result
end
function npartitions_with_zero(n::Int, m::Int)
if m == 0
if n == 0
return 1
else
return 0
end
else
return Combinatorics.npartitions(n + m, m)
end
end
print([A(n) for n in 1:46])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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