A289601 - OEIS

%I #11 Dec 16 2025 22:51:16

%S 1,1,1,3,10,34,114,382,1292,4426,15358,53915,191206,684103,2466416,

%T 8951932,32683216,119949930,442281014,1637618383,6086481702,

%U 22699003811,84918443200,318593346609,1198421583662,4518886787779,17077448924804,64671604514527,245380598678182,932708665735337

%N a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 431) or the same sequence for the mesh pattern (12, 491).

%H Christian Sievers, <a href="https://groups.google.com/g/seqfan/c/9jqIgQGj8Gg">RFE Dec 2025: Mesh patterns avoiding 321</a>, SeqFan thread.

%H Murray Tannock, <a href="https://skemman.is/bitstream/1946/25589/1/msc-tannock-2016.pdf">Equivalence classes of mesh patterns with a dominating pattern</a>, MSc Thesis, Reykjavik Univ., May 2016. See Appendix B2.

%F From _Thomas Scheuerle_, Dec 11 2025: (Start)

%F G.f.: (-(2*x^4)/(x - 1)^2 + (sqrt(1 - 4*x) - 1)*x^2 - sqrt(1 - 4*x) + 1)/(2*x).

%F a(n) = A289600(n)+1, for n > 2.

%F a(n) = A289595(n) + A289598(n) - A289590(n). (End)

%o (PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((-(2*x^4)/(x-1)^2+(sqrt(1-4*x)-1)*x^2-sqrt(1-4*x)+1)/(2*x)) \\ _Thomas Scheuerle_, Dec 11 2025

%Y Cf. A000108.

%Y Related to mesh patterns: A280891, A289446-A289453, A289587-A289616, A289652-A289654.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Jul 08 2017

%E More terms, name and offset changed by _Thomas Scheuerle_, Dec 11 2025