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a(n) = 4a(n-1) - 4a(n-2) + 3a(n-3) + a(n-4) - a(n-5).
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%I #18 Jul 14 2024 19:09:46

%S 1,2,5,14,42,128,389,1179,3572,10825,32810,99446,301412,913547,

%T 2768863,8392136,25435699,77092976,233660832,708201794,2146486339,

%U 6505777953,19718339694,59764246943,181139247400,549014312524,1664005563066

%N a(n) = 4a(n-1) - 4a(n-2) + 3a(n-3) + a(n-4) - a(n-5).

%C Arises in enumeration of certain pattern-avoiding permutations.

%H Z. Stankova and J. West, <a href="https://doi.org/10.1016/j.disc.2003.06.003">Explicit enumeration of 321, hexagon-avoiding permutations</a>, Discrete Math., 280 (2004), 165-189.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,3,1,-1).

%F G.f.: x*(1 - 2*x + x^2 - x^3 - x^4)/(1 - 4*x + 4*x^2 - 3*x^3 - x^4 + x^5). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009; corrected by _R. J. Mathar_, Sep 16 2009]

%p a[1]:=1: a[2]:=2: a[3]:=5: a[4]:=14: a[5]:=42: for n from 6 to 32 do a[n]:=4*a[n-1]-4*a[n-2]+3*a[n-3]+a[n-4]-a[n-5] od: seq(a[j],j=1..32); # _Emeric Deutsch_, Apr 12 2005

%t LinearRecurrence[{4,-4,3,1,-1},{1,2,5,14,42},40] (* _Harvey P. Dale_, Jul 14 2024 *)

%Y Cf. A058094, A092489-A092492.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Apr 04 2004

%E Edited by _Emeric Deutsch_, Apr 12 2005