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A363236 Number of permutations p of [n] such that each element in p has at least one neighbor with opposite parity. 3
1, 0, 2, 2, 16, 36, 288, 1152, 10368, 57600, 604800, 4320000, 51840000, 453600000, 6147187200, 63605606400, 962415820800, 11500218777600, 192255565824000, 2605984690176000, 47721518530560000, 723526168780800000, 14407079038894080000, 241602987041095680000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Wikipedia, Permutation
FORMULA
a(n) ~ phi^n * n! / (5^(1/4) * 2^(n-1)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, May 26 2023
EXAMPLE
a(0) = 1: (), the empty permutation.
a(1) = 0.
a(2) = 2: 12, 21.
a(3) = 2: 123, 321.
a(4) = 16: 1234, 1243, 1423, 1432, 2134, 2143, 2314, 2341, 3214, 3241, 3412, 3421, 4123, 4132, 4312, 4321.
a(5) = 36: 12345, 12354, 12534, 12543, 14325, 14352, 14523, 14532, 21345, 21543, 23145, 23541, 25143, 25341, 32145, 32154, 32514, 32541, 34125, 34152, 34512, 34521, 41325, 41523, 43125, 43521, 45123, 45321, 52134, 52143, 52314, 52341, 54123, 54132, 54312, 54321.
CROSSREFS
Sequence in context: A303567 A177832 A230800 * A076615 A098777 A127226
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 22 2023
STATUS
approved

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Last modified February 29 09:21 EST 2024. Contains 370418 sequences. (Running on oeis4.)