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%I #21 Oct 21 2022 22:08:34
%S 1,1,1,1,1,1,1,2,4,6,9,12,16,20,25,35,49,70,100,140,196,266,361,494,
%T 676,936,1296,1800,2500,3450,4761,6555,9025,12445,17161,23711,32761,
%U 45250,62500,86250,119025,164220,226576,312732,431649,595899,822649,1135564,1567504,2163456,2985984
%N 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=6, I={-1,1,2,3,4,5}.
%C a(n) is the number of subsets of {1,2,...,n-6} without differences equal to 2, 4 or 6.
%H G. C. Greubel, <a href="/A224808/b224808.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 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 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1,1,2,-1,1,0,0,-1,0,0, 1).
%F a(n) = a(n-1) + a(n-5) - a(n-6) + a(n-7) + 2*a(n-8) - a(n-9) + a(n-10) - a(n-13) + a(n-16).
%F G.f.: (1-x^5-x^8)/(1-x-x^5+x^6-x^7-2*x^8+x^9-x^10+x^13+x^16).
%F a(2*k-2) = (A003269(k))^2,
%F a(2*k-1) = A003269(k) * A003269(k+1)
%t CoefficientList[Series[(1 - x^5 - x^8)/(1 - x - x^5 + x^6 - x^7 - 2*x^8 + x^9 - x^10 + x^13 + x^16), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 28 2017 *)
%o (PARI) x='x+O('x^66); Vec((1-x^5-x^8)/(1-x-x^5+x^6-x^7-2*x^8+x^9-x^10+x^13+x^16) ) \\ _Joerg Arndt_, Apr 19 2013
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694.
%K nonn,easy
%O 0,8
%A _Vladimir Baltic_, Apr 18 2013
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