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A045678
Number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement, but not equivalent to their reverse and complement.
3
0, 0, 0, 2, 4, 12, 26, 56, 116, 240, 492, 992, 2010, 4032, 8120, 16256, 32628, 65280, 130800, 261632, 523756, 1047552, 2096096, 4192256, 8386522, 16773120, 33550272, 67100672, 134209464, 268419072, 536854400, 1073709056, 2147450740
OFFSET
0,4
COMMENTS
The number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement is A011782(n) and those which are equivalent to their reverse, complement and reversed complement is A045674(n). - Andrew Howroyd, Sep 28 2017
FORMULA
a(2n+1) = A020522(n) = 4^n - 2^n. - Max Alekseyev, Jan 13 2006
a(n) = A011782(n) - A045674(n). - Andrew Howroyd, Sep 28 2017
MATHEMATICA
(* b = A011782, c = A045674 *)
b[0] = 1; b[n_] := 2^(n - 1);
c[0] = 1; c[n_] := c[n] = If[EvenQ[n], 2^(n/2-1) + c[n/2], 2^((n-1)/2)];
a[n_] := b[n] - c[n];
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Oct 08 2017, after Andrew Howroyd *)
CROSSREFS
Sequence in context: A136253 A266079 A284125 * A236002 A291406 A219752
KEYWORD
nonn
STATUS
approved