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 A381859 #23 May 13 2025 09:46:53
%S A381859 1,1,2,5,11,23,50,109,236,511,1108,2402,5206,11284,24459,53016,114914,
%T A381859 249081,539894,1170243,2536551,5498082,11917326,25831309,55990457,
%U A381859 121361689,263056605,570186341,1235903062,2678872272,5806569196,12585984849,27280655629
%N A381859 a(n) is the number of permutations that avoid 312 and 4321 and whose square avoids 321.
%H A381859 Michael De Vlieger, <a href="/A381859/b381859.txt">Table of n, a(n) for n = 0..2977</a>
%H A381859 Kassie Archer and Noel Bourne, <a href="https://arxiv.org/abs/2505.05218">Pattern avoidance in compositions and powers of permutations</a>, arXiv:2505.05218 [math.CO], 2025. See p. 8.
%H A381859 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,0,-1).
%F A381859 G.f.: (1-x)/(1-2*x-x^3+x^5).
%F A381859 a(n) = a(n-3) + a(n-4) + Sum_{j=0..n-1} a(j).
%e A381859 The 11 permutations of length 4 are: 1234, 1243, 1324, 1342, 1432, 2134, 2143, 2314, 2341, 3214, 3421.
%t A381859 CoefficientList[Series[(1 - x)/(1 - 2*x - x^3 + x^5), {x, 0, 32}], x] (* _Michael De Vlieger_, May 13 2025 *)
%Y A381859 Cf. A001590 (with square avoiding 312), A001590 (with square avoiding 132).
%K A381859 nonn,easy
%O A381859 0,3
%A A381859 _Kassie Archer_, Mar 10 2025