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A350028
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Number of Euler tours of the complete graph on n vertices (minus a matching if n is even).
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9
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OFFSET
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3,1
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LINKS
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FORMULA
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EXAMPLE
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For n=6, if the edges 12,34,56 are removed from the complete graph and we fix
the tour to start with the edge 13, we get 372 Euler tours. Here are the first and the last few in lexicographic order.
1324152635461
1324152645361
1324153625461
1324153645261
1324154625361
1324154635261
1324162536451
...
1364532516241
1364532614251
1364532615241.
This must be multiplied by 2 to account for the reversed tours, for a total of 744.
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PROG
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(Python)
# for 3 <= n <= 9
def A(n, w="13"):
if n%2==0 and len(w) > n*(n-1)//2 - n//2: return 2
if n%2==1 and len(w) > n*(n-1)//2: return 2
return sum(A(n, w+t) for t in "123456789"[:n]
if t!=w[-1] and t+w[-1] not in w and w[-1]+t not in w
and (n%2==1 or t+w[-1] not in "121 343 565 787"))
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CROSSREFS
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KEYWORD
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nonn,walk,hard,more
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AUTHOR
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STATUS
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approved
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