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A072850 Number of permutations satisfying i-2<=p(i)<=i+4, i=1..n.

%I A072850 #18 Feb 21 2025 12:34:56
%S A072850 1,2,6,18,54,146,391,1081,3004,8320,22984,63424,175176,484113,1337721,
%T A072850 3695886,10210702,28209954,77940078,215337554,594943087,1643728129,
%U A072850 4541349672,12547013504,34665373744,95774808224,264610227072
%N A072850 Number of permutations satisfying i-2<=p(i)<=i+4, i=1..n.
%H A072850 R. H. Hardin, <a href="/A072850/b072850.txt">Table of n, a(n) for n=1..400</a>
%H A072850 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 A072850 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 4, 6, 10, 12, -4, -6, -6, 0, -2, -2, 0, 1, 1).
%F A072850 Recurrence: a(n) = a(n - 1) + 2*a(n - 2) + 4*a(n - 3) + 6*a(n - 4) + 10*a(n - 5) + 12*a(n - 6) - 4*a(n - 7) - 6*a(n - 8) - 6*a(n - 9) - 2*a(n - 11) - 2*a(n - 12) + a(n - 14) + a(n - 15).
%F A072850 G.f.: - (x^9 + x^7 - 2*x^6 - 2*x^4 - 2*x^3 - x^2 + 1)/(x^15 + x^14 - 2*x^12 - 2*x^11 - 6*x^9 - 6*x^8 - 4*x^7 + 12*x^6 + 10*x^5 + 6*x^4 + 4*x^3 + 2*x^2 + x - 1)
%Y A072850 Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K A072850 nonn,easy
%O A072850 1,2
%A A072850 _Vladimir Baltic_, Jul 25 2002