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A296531
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Number of non-averaging permutations of [n] with first element ceiling(n/2).
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2
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1, 1, 1, 2, 3, 6, 13, 32, 51, 76, 161, 386, 903, 2280, 5018, 12828, 19720, 27656, 48788, 100120, 220686, 537208, 1258242, 3123166, 7056165, 17189752, 35968308, 82137764, 189847917, 509880208, 1322092262, 3807727932, 5678509066, 7721623440, 13293899416, 23650787296
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OFFSET
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0,4
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COMMENTS
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A non-averaging permutation avoids any 3-term arithmetic progression.
a(0) = 1 by convention.
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 6: 31254, 31524, 31542, 35124, 35142, 35412.
a(6) = 13: 312564, 315264, 315426, 315462, 315624, 351264, 351426, 351462, 351624, 354126, 354162, 354612, 356124.
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MAPLE
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b:= proc(s) option remember; local n, r, ok, i, j, k;
if nops(s) = 1 then 1
else n, r:= max(s), 0;
for j in s minus {n} do ok, i, k:= true, j-1, j+1;
while ok and i>=0 and k<n do ok, i, k:=
not i in s xor k in s, i-1, k+1 od;
r:= r+ `if`(ok, b(s minus {j}), 0)
od; r
fi
end:
a:= n-> b({$0..n} minus {ceil(n/2)-1}):
seq(a(n), n=0..25);
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MATHEMATICA
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b[s_] := b[s] = Module[{n = Max[s], r = 0, ok, i, j, k}, If[Length[s] == 1, 1, Do[{ok, i, k} = {True, j - 1, j + 1}; While[ok && i >= 0 && k < n, {ok, i, k} = {FreeQ[s, i] ~Xor~ MemberQ[s, k], i - 1, k + 1}]; r = r + If[ok, b[s ~Complement~ {j}], 0], {j, s ~Complement~ {n}}]; r]];
a[n_] := b[Complement[Range[0, n], {Ceiling[n/2] - 1}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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