A378005 - OEIS

%I #8 Dec 03 2024 12:40:28

%S 1,0,0,0,0,0,1,1,0,0,0,0,1,3,1,0,0,0,1,6,6,1,0,0,1,10,20,10,1,1,1,15,

%T 50,50,15,6,7,21,105,175,105,36,42,49,196,490,490,231,183,217,392,

%U 1176,1764,1246,785,946,1141,2646,5292,5418,3613,3664,4390,6601,14112,19614

%N Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-2,4,5} for all i=1,...,n.

%D D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), North-Holland, Amsterdam, 1970, pp. 755-770.

%H Michael A. Allen and Kenneth Edwards, <a href="https://doi.org/10.1080/03081087.2022.2107979">Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices</a>, Lin. Multilin. Alg. 72:13 (2024) 2091-2103.

%H V. Baltic, <a href="http://pefmath.etf.rs/vol4num1/AADM-Vol4-No1-119-135.pdf">On the number of certain types of strongly restricted permutations</a>, Applicable Analysis and Discrete Mathematics, 4(1) (2010), 119-135.

%H Kenneth Edwards and Michael A. Allen, <a href="https://doi.org/10.1016/j.dam.2015.02.004">Strongly restricted permutations and tiling with fences</a>, Discrete Applied Mathematics, 187 (2015), 82-90.

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,2,3,0,-2,-2,0,-1,-2,-3,1,1,1,0,0,0,1).

%F a(n) = a(n-3) + 2*a(n-6) + 3*a(n-7) - 2*a(n-9) - 2*a(n-10) - a(n-12) - 2a(n-13) - 3*a(n-14) + a(n-15) + a(n-16) + a(n-17) + a(n-21) for n >= 21.

%F G.f.: (1 - x)*(1 + x + x^2 - x^6 - 3*x^7 - 3*x^8 - 2*x^9 - x^10 - x^11 - x^12 - x^13)/(1 - x^3 - 2*x^6 - 3*x^7 + 2*x^9 + 2*x^10 + x^12 + 2*x^13 + 3*x^14 - x^15 - x^16 - x^17 - x^21).

%e a(6) = 1: 561234.

%e a(7) = 1: 6712345.

%t CoefficientList[Series[1/((1-x^7-x^6-x^13/(1-x^7-x^6/(1-x^7/(1-x^3))))), {x, 0, 65}],x]

%Y See A376743 for other sequences related to strongly restricted permutations.

%Y Cf. A377715, A001263.

%K easy,nonn

%O 0,14

%A _Michael A. Allen_, Nov 13 2024