1 , 2 , 9 , 4 4 , 2 6 5 , ?
What is the next number in the above sequence?
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This problem has been posted several times... @Geoff Pilling
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Yup, its similar to this one. :^)
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Well, I guess it's not unique. It's still a great problem though!
Also known as subfactorials.
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Yep! Subfactorials it is.
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Nice problem! It's... unique! :)
Cool !!! Nice question! (Ps. I got it !! Haha)
( 1 ×3)-1 => ( 2 ×4)+1 => ( 9 ×5)-1 => ( 4 4 => ( 4 4 ×6)+1 => ( 2 6 5 ×7)-1 = 1 8 5 4 .
Hi. Let's suppose that a 1 = 1 , a 2 = 2 we got a n = n ∗ ( a n − 1 + a n − 2 ) that suits, thus a 6 = 6 ∗ ( 4 4 + 2 6 5 ) = 1 8 5 4
Good job observing the recurrence relation, Marc. The term, a n , denotes the number of derangements of n distinct objects. Could you prove this recurrence relation using a combinatorial approach?
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The terms of the pattern are the number of Derangements of Natural numbers
Thus the next term is 7 ! × ( 2 1 − 6 1 + 2 4 1 − 1 2 0 1 + 7 2 0 1 − 5 0 4 0 1 ) = 1 8 5 4 □