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A076220
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Number of permutations of 1..n in which every pair of adjacent numbers are relatively prime.
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11
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1, 2, 6, 12, 72, 72, 864, 1728, 13824, 22032, 555264, 476928, 17625600, 29599488, 321115392, 805146624, 46097049600, 36481536000, 2754120268800, 3661604352000, 83905105305600, 192859121664000, 20092043520000000, 15074060547686400
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..24.
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FORMULA
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a(p-1)=A086595(p) for prime p. - Max Alekseyev, Jun 12 2005
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EXAMPLE
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a(4) = 12 since there are 12 permutations of 1234 in which every 2 adjacent numbers are relatively prime: 1234, 1432, 2134, 2143, 2314, 2341, 3214, 3412, 4123, 4132, 4312, 4321
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MAPLE
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with (combinat): for n from 1 to 7 do P:=permute(n): ct:=0: for j from 1 to n! do if add(gcd(P[j][i+1], P[j][i]), i=1..n-1)=n-1 then ct:=ct+1 else ct:=ct fi od: a[n]:=ct: od: seq(a[n], n=1..7); (Deutsch)
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MATHEMATICA
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f[n_] := Block[{p = Permutations[ Table[i, {i, 1, n}]], c = 0, k = 1}, While[k < n! + 1, If[ Union[ GCD @@@ Partition[p[[k]], 2, 1]] == {1}, c++ ]; k++ ]; c]; Do[ Print[ f[n]], {n, 2, 15}]
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PROG
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(PARI) {A076220(n)=local(A, d, n, r, M); A=matrix(n, n, i, j, if(gcd(i, j)==1, 1, 0)); r=0; for(s=1, 2^n-1, M=vecextract(A, s, s)^(n-1); d=matsize(M)[1]; r+=(-1)^(n-d)*sum(i=1, d, sum(j=1, d, M[i, j]))); r} (Alekseyev)
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CROSSREFS
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Cf. A086595.
Sequence in context: A106037 A136240 A090747 * A178846 A173843 A107763
Adjacent sequences: A076217 A076218 A076219 * A076221 A076222 A076223
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KEYWORD
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nonn
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AUTHOR
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Lior Manor Nov 04 2002
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EXTENSIONS
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Extended by Frank Ruskey, Nov 11 2002
a(15)=321115392 and a(16)=805146624 from Ray Chandler and Joshua Zucker, Apr 10 2005
Many further terms from Max Alekseyev, Jun 12 2005
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STATUS
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approved
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