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%I #13 Jul 17 2024 18:09:24
%S 1,1,2,6,24,120,718,4914,37300,308460,2748354,26194542,265691456,
%T 2856606480,32449828310,388371994890,4885210675692,64439603536980,
%U 889564376280586,12827733624005958,192897097090449208,3020051018689640760,49155675298520617182,830625328754347651746
%N Number of permutations of {1..n} with fewer than 4 interior elements having values lying between the values of their neighbors.
%H Alois P. Heinz, <a href="/A226437/b226437.txt">Table of n, a(n) for n = 0..482</a> (terms n = 1..210 from R. H. Hardin)
%e Some solutions for n=8:
%e ..3....8....1....8....2....4....2....8....4....5....8....7....6....6....7....2
%e ..7....1....2....5....7....3....5....4....7....7....3....1....3....8....3....8
%e ..1....2....8....6....3....8....4....7....8....1....4....4....7....4....4....6
%e ..2....4....6....3....6....7....8....5....3....2....6....3....5....7....5....3
%e ..8....5....3....1....8....2....1....1....2....4....1....2....4....3....6....5
%e ..6....3....5....2....4....5....3....2....6....3....2....5....8....1....1....1
%e ..4....6....4....7....5....6....6....3....5....8....7....6....2....5....8....4
%e ..5....7....7....4....1....1....7....6....1....6....5....8....1....2....2....7
%Y Column 4 of A226441.
%K nonn
%O 0,3
%A _R. H. Hardin_, Jun 06 2013
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 17 2024