login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079987 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-1,0,2}. 0

%I #15 Jul 31 2015 12:22:33

%S 1,0,0,1,2,3,5,7,15,29,49,84,149,268,484,855,1508,2684,4784,8516,

%T 15134,26873,47782,85004,151149,268704,477685,849299,1510163,2685089,

%U 4773851,8487625,15090786,26831239,47705352,84818268,150803857,268125092

%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-1,0,2}.

%C Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,0,1}.

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

%H Vladimir 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 Vol. 4, No 1 (2010), 119-135

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (2, -2, 3, -2, 4, -1, -2, 4, -5, 4, -6, 3, 0, -2, 1, -2, 2, -1).

%F a(n) = 2*a(n-1) -2*a(n-2) +3*a(n-3) -2*a(n-4) +4*a(n-5) -a(n-6) -2*a(n-7) +4*a(n-8) -5*a(n-9) +4*a(n-10) -6*a(n-11) +3*a(n-12) -2*a(n-14) +a(n-15) -2*a(n-16) +2*a(n-17) -a(n-18).

%F G.f.: -(x^12-2*x^11 +2*x^10-2*x^9 +2*x^8-x^7 -x^6+3*x^5 -2*x^4+2*x^3 -2*x^2+2*x -1)/( x^18 -2*x^17 +2*x^16 -x^15 +2*x^14 -3*x^12 +6*x^11 -4*x^10 +5*x^9 -4*x^8 +2*x^7 +x^6 -4*x^5 +2*x^4 -3*x^3 +2*x^2 -2*x+1)

%t LinearRecurrence[{2,-2,3,-2,4,-1,-2,4,-5,4,-6,3,0,-2,1,-2,2,-1},{1,0,0,1,2,3,5,7, 15,29, 49,84,149,268,484,855,1508,2684},40] (* _Harvey P. Dale_, Apr 29 2011 *)

%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

%K nonn

%O 0,5

%A _Vladimir Baltic_, Feb 17 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)