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Number of permutations of {1..n} with fewer than 3 interior elements having values lying between the values of their neighbors.
1

%I #9 Jul 17 2024 18:56:27

%S 1,1,2,6,24,118,658,4078,27724,205134,1641534,14132390,130299584,

%T 1281352790,13391026730,148237230942,1733059331604,21341010960286,

%U 276120222880246,3745333514843734,53149568086851784,787599172764342822,12166057777073762082

%N Number of permutations of {1..n} with fewer than 3 interior elements having values lying between the values of their neighbors.

%H Alois P. Heinz, <a href="/A226436/b226436.txt">Table of n, a(n) for n = 0..483</a> (terms n = 1..210 from R. H. Hardin)

%e Some solutions for n=9

%e ..6....4....3....9....7....7....9....5....8....8....1....8....8....7....6....2

%e ..1....2....2....2....3....4....3....3....1....4....4....3....4....1....4....1

%e ..3....8....8....1....2....8....4....9....9....3....3....9....2....2....8....7

%e ..9....3....7....6....8....3....2....1....4....7....5....5....9....6....5....9

%e ..5....7....5....5....5....5....5....8....6....6....2....7....1....3....9....3

%e ..2....9....6....3....1....9....7....2....7....2....8....4....5....5....2....6

%e ..8....1....4....7....6....1....6....7....3....9....9....6....3....8....3....4

%e ..4....5....9....4....4....6....1....4....5....1....7....2....6....4....1....5

%e ..7....6....1....8....9....2....8....6....2....5....6....1....7....9....7....8

%Y Column 3 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