%I #16 Jun 19 2024 18:58:47
%S 1,4,32,392,6488,135360,3408120,100520432,3398723928,129588803696,
%T 5500585388616,257232445666832
%N Number of pairs of length n permutations achievable by double-ended priority queue.
%H Sean A. Irvine, <a href="/A007763/a007763.pdf">Notes on A007763</a>
%H M. D. Atkinson and R. Beals, <a href="https://www.cs.otago.ac.nz/staffpriv/mike/Papers/PriorityQueues/PQs-Beals.pdf">Priority queues and permutations</a>, SIAM J. Comput. 23 (1994), 1225-1230.
%e From _Bert Dobbelaere_, Jun 18 2024: (Start)
%e The input {2,1,4,3} can be reordered to {4,1,3,2} via the DEPQ using the following sequence of operations:
%e insert(2)
%e insert(1)
%e insert(4)
%e readMax() => 4
%e readMin() => 1
%e insert(3)
%e readMax() => 3
%e readMin() => 2
%e Of the (4!)^2 possible (input,output) pairs, only 392 can be achieved with a valid operation sequence, hence a(4) = 392. (End)
%Y Cf. A000272 (single-ended priority queue).
%K nonn,more
%O 1,2
%A mda(AT)cs.st-andrews.ac.uk (Michael Atkinson)
%E Title improved and a(7)-a(9) from _Sean A. Irvine_, Jan 23 2018
%E a(10)-a(12) from _Bert Dobbelaere_, Jun 18 2024