A080013 - OEIS

%I #31 May 20 2026 07:59:55

%S 1,0,0,1,1,1,1,3,3,4,6,9,12,16,24,33,46,64,91,127,177,249,349,489,684,

%T 960,1345,1884,2640,3700,5185,7264,10180,14265,19989,28009,39249,

%U 54999,77067,107992,151326,212049,297136,416368,583444,817561,1145622,1605324,2249491,3152139,4416993

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

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

%D Allen, Michael A., and Kenneth Edwards. "Identities relating permanents of some classes of (0, 1) Toeplitz matrices to generalized Fibonacci numbers." The Fibonacci Quarterly 63.2 (2025): 163-177.

%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 Michael De Vlieger, <a href="/A080013/b080013.txt">Table of n, a(n) for n = 0..6829</a>

%H Michael A. Allen and Kenneth Edwards, <a href="https://arxiv.org/abs/2107.02589">Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices</a>, arXiv:2107.02589 [math.CO], 2021.

%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 Tomislav Došlić, Mate Puljiz, Stjepan Šebek, and Josip Žubrinić, <a href="https://arxiv.org/abs/2210.12411">On a variant of Flory model</a>, arXiv:2210.12411 [math.CO], 2022.

%H P. L. Krapivsky and J. M. Luck, <a href="https://arxiv.org/abs/2211.12815">Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model</a>, arXiv:2211.12815 [cond-mat.stat-mech], 2022.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,0,-1).

%F Recurrence: a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-6).

%F G.f.: -(x^2-1)/(x^6-x^4-x^3-x^2+1)

%t LinearRecurrence[{0,1,1,1,0,-1},{1,0,0,1,1,1},60] (* _Harvey P. Dale_, Aug 08 2019 *)

%o (PARI) a(n)=([0,1,0,0,0,0; 0,0,1,0,0,0; 0,0,0,1,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1; -1,0,1,1,1,0]^n*[1;0;0;1;1;1])[1,1] \\ _Charles R Greathouse IV_, May 20 2026

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

%K nonn,easy

%O 0,8

%A _Vladimir Baltic_, Jan 24 2003