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EXAMPLE
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The a(2) = 1 through a(5) = 14 partitions (A = 10):
(4) (6) (8) (A)
(4,2) (4,4) (5,5)
(5,1) (5,3) (6,4)
(6,2) (7,3)
(7,1) (8,2)
(5,2,1) (9,1)
(6,1,1) (5,3,2)
(5,4,1)
(6,2,2)
(6,3,1)
(7,2,1)
(8,1,1)
(6,2,1,1)
(7,1,1,1)
For example, the seven normal loop-multigraphs with degrees y = (5,3,2) are:
{{1,1},{1,1},{1,2},{2,2},{3,3}}
{{1,1},{1,1},{1,2},{2,3},{2,3}}
{{1,1},{1,1},{1,3},{2,2},{2,3}}
{{1,1},{1,2},{1,2},{1,2},{3,3}}
{{1,1},{1,2},{1,2},{1,3},{2,3}}
{{1,1},{1,2},{1,3},{1,3},{2,2}}
{{1,2},{1,2},{1,2},{1,3},{1,3}},
but since none of these is a loop-graph (because they are not strict), y is counted under a(5).
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