cp's OEIS Frontend

A249560 Number of length n permutations avoiding (231,{1},{}) and (132,{},{2}).

%I A249560 #29 Sep 27 2016 14:17:46
%S A249560 1,1,2,4,9,22,58,163,485,1519,4985,17077,60871,225152,862150,3410641,
%T A249560 13913800,58440010,252348913,1118802690,5086910935,23693925911,
%U A249560 112947299251,550527774738,2741489275969,13936841789100,72277551806634,382134348251357,2058420014680378
%N A249560 Number of length n permutations avoiding (231,{1},{}) and (132,{},{2}).
%C A249560 (231,{1},{}) is a vincular pattern. It has underlying classical pattern 231 and the extra requirement that the 2 and the 3 are adjacent in the permutation.
%C A249560 (132,{},{2}) is a co-vincular pattern. It has underlying classical pattern 132 and the extra requirement that the 2 and 3 are exactly one apart in the permutation.
%H A249560 Alois P. Heinz, <a href="/A249560/b249560.txt">Table of n, a(n) for n = 0..300</a>
%H A249560 Christian Bean, A Claesson, H Ulfarsson, <a href="http://arxiv.org/abs/1512.03226">Simultaneous Avoidance of a Vincular and a Covincular Pattern of Length 3</a>, arXiv preprint arXiv:1512.03226, 2015
%F A249560 if i = 1: a(n,k,i) = sum( a(n-1,k,j) for j in [1..k] )
%F A249560 if i = k: a(n,k,i) = sum( a(n-1,k-1,j) + a(n-1,k,j) for j in [1..k-1] )
%F A249560 otherwise: a(n,k,i) = sum( a(n-1,k,j) for j in [1..i-1] )
%F A249560 where n is the length, k is the number of right to left minima and i is the position of the maximum in relation to the right to left minima.
%F A249560 Initial Conditions: if k > n or i > k then a(n,k,i) = 0, if k = 1 then a(n,k,i) = 1.
%F A249560 Then a(n) = sum( sum( a(n,k,i) for i in [1..k]) for k in [1..n] ).
%F A249560 G.f: 1 + x * sum(x^n * F_n(1+x) for n >= 0) where F_n(q) = sum( [n,m] for m in [0..n] ). Note [n,m] is the q-binomial. - _Christian Bean_, Jun 03 2015
%Y A249560 Cf. A249561, A249562, A249563.
%K A249560 nonn
%O A249560 0,3
%A A249560 _Christian Bean_, Nov 01 2014
%E A249560 More terms from _Alois P. Heinz_, Nov 01 2014