A New Quantity Counted by OEIS Sequence A006012

Abstract

We prove an existing conjecture that the sequence defined recursively by $a_1=1,a_2=2,a_n=4a_{n-1}-2a_{n-2}$ counts the number of length-$n$ permutations avoiding the four generalized permutation patterns 1-32-4, 1-42-3, 2-31-4, and 2-41-3.