This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A092493 #18 Jul 14 2024 19:09:46
%S A092493 1,2,5,14,42,128,389,1179,3572,10825,32810,99446,301412,913547,
%T A092493 2768863,8392136,25435699,77092976,233660832,708201794,2146486339,
%U A092493 6505777953,19718339694,59764246943,181139247400,549014312524,1664005563066
%N A092493 a(n) = 4a(n-1) - 4a(n-2) + 3a(n-3) + a(n-4) - a(n-5).
%C A092493 Arises in enumeration of certain pattern-avoiding permutations.
%H A092493 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 A092493 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,3,1,-1).
%F A092493 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 A092493 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 A092493 LinearRecurrence[{4,-4,3,1,-1},{1,2,5,14,42},40] (* _Harvey P. Dale_, Jul 14 2024 *)
%Y A092493 Cf. A058094, A092489-A092492.
%K A092493 nonn,easy
%O A092493 1,2
%A A092493 _N. J. A. Sloane_, Apr 04 2004
%E A092493 Edited by _Emeric Deutsch_, Apr 12 2005