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Burkard Polster, <a href="https://www.youtube.com/watch?v=phqXU-1CFas">What's the next freak identity? A new deep connection with Sophie Germain primes</a>, YouTube Mathologer video, 2024.
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1, 0, 1, 0, 8, 0, 1024, 0, 2097152, 0, 68719476736, 0, 36028797018963968, 0, 302231454903657293676544, 0, 40564819207303340847894502572032, 0, 87112285931760246646623899502532662132736, 0, 2993155353253689176481146537402947624255349848014848
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(Maxima) a(n):=if n=0 then 1 else if oddp(n) then 0 else 2^((n-1)*(n-2)/2);
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a(n) is the number of subgraphs of the complete graph K[n], where the degree of all nodes is odd.
1, 0, 1, 0, 8, 0, 1024, 0, 2097152, 0, 68719476736, 0, 36028797018963968, 0, 302231454903657293676544, 0, 40564819207303340847894502572032, 0
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If n=0, a(n)=1. If n is odd, a(n)=0. If n>0 is even, a(n)=2^((n-1)*(n-2)/2).
For n = 4, there are eight such graphs:
A-B A-B A B A B A-B A B A B A-B
|\ /| |/ \| | | X |X|
C D C D C-D C-D C-D C D C D C-D
A006125 gives the corresponding sequence for the case where the degree of all nodes is even.
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easy,nonn
Douglas Boffey, Oct 09 2024
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