cp's OEIS Frontend

A224809 Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=2, r=4, I={-1,1,2,3}.

%I A224809 #61 Dec 04 2023 10:52:43
%S A224809 1,1,1,1,1,2,4,6,9,12,16,24,36,54,81,117,169,247,361,532,784,1148,
%T A224809 1681,2460,3600,5280,7744,11352,16641,24381,35721,52353,76729,112462,
%U A224809 164836,241570,354025,518840,760384,1114416,1633284
%N A224809 Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=2, r=4, I={-1,1,2,3}.
%C A224809 Number of subsets of {1,2,...,n-4} without differences equal to 2 or 4.
%H A224809 Gheorghe Coserea, <a href="/A224809/b224809.txt">Table of n, a(n) for n = 0..4096</a>
%H A224809 Michael A. Allen, <a href="https://arxiv.org/abs/2209.01377">On a Two-Parameter Family of Generalizations of Pascal's Triangle</a>, arXiv:2209.01377 [math.CO], 2022.
%H A224809 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 (April, 2010), 119-135
%H A224809 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,1,0,0,-1).
%F A224809 a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-5) + a(n-6) - a(n-9).
%F A224809 G.f.: -(x-1)*(1+x+x^2) / ( (x^3+x-1)*(x^6-x^4-1) ).
%F A224809 a(2*k) = (A000930(k))^2, a(2*k+1) = A000930(k) * A000930(k+1).
%t A224809 CoefficientList[Series[-(x-1)*(1+x+x^2)/((x^3+x-1)*(x^6-x^4-1)), {x, 0, 50}], x] (* _G. C. Greubel_, Apr 28 2017 *)
%o A224809 (PARI)
%o A224809 N = 42; x = 'x + O('x^N);
%o A224809 Vec(Ser(-(x-1)*(1+x+x^2)/((x^3+x-1)*(x^6-x^4-1))))  \\ _Gheorghe Coserea_, Nov 11 2016
%Y A224809 Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694, A224808.
%K A224809 nonn
%O A224809 0,6
%A A224809 _Vladimir Baltic_, May 16 2013