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 A242530 Number of cyclic arrangements of S={1,2,...,2n} such that the binary expansions of any two neighbors differ by one bit. 16
 0, 0, 1, 0, 2, 8, 0, 0, 224, 754, 0, 26256, 0, 0, 22472304, 0, 90654576, 277251016, 0, 7852128780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Here, a(n)=NPC(2n;S;P) is the count of all neighbor-property cycles for a specific set S of 2n elements and a pair-property P. For more details, see the link and A242519. In this case the property P is the Gray condition. The choice of the set S is important; when it is replaced by {0,1,2,...,2n-1}, the sequence changes completely and becomes A236602. LINKS S. Sykora, On Neighbor-Property Cycles, Stan's Library, Volume V, 2014. EXAMPLE The two cycles for n=5 (cycle length 10) are: C_1={1,3,7,5,4,6,2,10,8,9}, C_2={1,5,4,6,7,3,2,10,8,9}. MATHEMATICA A242530[n_] := Count[Map[lpf, Map[j1f, Permutations[Range[2, 2 n]]]], 0]/2; j1f[x_] := Join[{1}, x, {1}]; btf[x_] := Module[{i},    Table[DigitCount[BitXor[x[[i]], x[[i + 1]]], 2, 1], {i,      Length[x] - 1}]]; lpf[x_] := Length[Select[btf[x], # != 1 &]]; Table[A242530[n], {n, 1, 5}] (* OR, a less simple, but more efficient implementation. *) A242530[n_, perm_, remain_] := Module[{opt, lr, i, new},    If[remain == {},      If[DigitCount[BitXor[First[perm], Last[perm]], 2, 1] == 1, ct++];      Return[ct],      opt = remain; lr = Length[remain];      For[i = 1, i <= lr, i++,       new = First[opt]; opt = Rest[opt];       If[DigitCount[BitXor[Last[perm], new], 2, 1] != 1, Continue[]];       A242530[n, Join[perm, {new}],        Complement[Range[2, 2 n], perm, {new}]];       ];      Return[ct];      ];    ]; Table[ct = 0; A242530[n, {1}, Range[2, 2 n]]/2, {n, 1, 10}] (* Robert Price, Oct 25 2018 *) PROG (C++) See the link. CROSSREFS Cf. A236602, A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242531, A242532, A242533, A242534. Sequence in context: A095217 A230915 A242922 * A073410 A021361 A199156 Adjacent sequences:  A242527 A242528 A242529 * A242531 A242532 A242533 KEYWORD nonn,hard,more AUTHOR Stanislav Sykora, May 30 2014 EXTENSIONS a(16)-a(20) from Fausto A. C. Cariboni, May 10 2017, May 15 2017 STATUS approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)