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%I #26 Jan 06 2016 12:07:02
%S 1,0,1,2,9,44,265,1854,4752,12072,30500,76038,190656,481318,1224852,
%T 3117528,7944464,20283046,51912320,133129054,341972624,879678624,
%U 2266157892,5846150862,15101728320,39058470566,101135401556,262158219552,680253580304,1766843951390
%N Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by three: p(i)<>i and (i-p(i) mod n <= 3 or p(i)-i mod n <= 3).
%C a(n) = A000166(n) for n <= 7.
%H Alois P. Heinz, <a href="/A260081/b260081.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: -(631*x^43 +953*x^42 -174*x^41 -3296*x^40 -6097*x^39 -3581*x^38 -11543*x^37 -14483*x^36 +3789*x^35 +67487*x^34 +120551*x^33 +88025*x^32 +64863*x^31 +14567*x^30 -69173*x^29 -386577*x^28 -600146*x^27 -488818*x^26 -105459*x^25 +188333*x^24 +315070*x^23 +540030*x^22 +633950*x^21 +478098*x^20 +53481*x^19 -202345*x^18 -260532*x^17 -228778*x^16 -157245*x^15 -78737*x^14 +1943*x^13 +17159*x^12 +13669*x^11 +7299*x^10 +3547*x^9 +981*x^8 -1103*x^7 -151*x^6 -25*x^5 -5*x^4 +3*x -1) / ((x-1) *(x+1) *(x^2+x+1) *(x^2-x+1) *(x^13-x^11+x^10-x^9-x^8-9*x^7 -3*x^6+3*x^5+7*x^4-x^3+x^2+2*x-1) *(x^3+x^2+x-1) *(x^3-x^2-x-1) *(x^12+x^11+x^10-x^8+x^7-8*x^6-7*x^5-5*x^4-2*x^3-x^2-x+1)).
%e a(8) = 4752: 21436587, 21436785, 21436857, 21437586, ..., 87653421, 87654123, 87654312, 87654321.
%p a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
%p `if`(i<>j and (i-j mod n<=3 or j-i mod n<=3), 1, 0)))):
%p seq(a(n), n=0..15);
%t a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 3 || Mod[j - i, n] <= 3), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Jan 06 2016, adapted from Maple *)
%Y Cf. A000166, A260074, A260092, A260094, A260111, A260091, A260115, A257953, A260216.
%Y Cf. A079997.
%K nonn,easy
%O 0,4
%A _Alois P. Heinz_, Jul 15 2015
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