A079996 - OEIS

%I #11 Jul 30 2024 13:38:18

%S 1,1,1,3,11,33,82,198,516,1389,3690,9642,25143,65867,173092,454578,

%T 1192227,3125940,8198836,21509532,56429115,148023671,388279519,

%U 1018515853,2671777153,7008626377,18384947908,48227023198,126508325008

%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}.

%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={-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 4 (2010), 119-135

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 3, 4, 9, 9, -15, -12, 0, 7, -6, -6, 5, 5, 3, -2, -1, 2, -1, -1).

%F a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +4*a(n-4) +9*a(n-5) +9*a(n-6) -15*a(n-7) -12*a(n-8) +7*a(n-10) -6*a(n-11) -6*a(n-12) +5*a(n-13) +5*a(n-14) +3*a(n-15) -2*a(n-16) -a(n-17) +2*a(n-18) -a(n-19) -a(n-20).

%F G.f.: -(x^14 -2*x^12 +x^11 -x^10 -2*x^8 -2*x^7 +4*x^6 +x^4 +3*x^3 +2*x^2-1) /(x^20 +x^19 -2*x^18 +x^17 +2*x^16 -3*x^15 -5*x^14 -5*x^13 +6*x^12 +6*x^11 -7*x^10 +12*x^8 +15*x^7 -9*x^6 -9*x^5 -4*x^4 -3*x^3 -2*x^2 -x+1)

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

%K nonn

%O 0,4

%A _Vladimir Baltic_, Feb 17 2003