A372256 a(n) = (n-1)!/2^floor((n-1)/2) + floor((n-1)/2).

1, 1, 2, 4, 8, 32, 93, 633, 2524, 22684, 113405, 1247405, 7484406, 97297206, 681080407, 10216206007, 81729648008, 1389404016008, 12504636144009, 237588086736009, 2375880867360010, 49893498214560010, 548828480360160011, 12623055048283680011, 151476660579404160012

Offset

1,3

Comments

The maximum number of distinct cards in a deck that has each card twice to perform the n-card trick, where the audience chooses the hidden card.

Links

Table of n, a(n) for n=1..25.

Michael Kleber and Ravi Vakil, The best card trick, The Mathematical Intelligencer 24 (2002), 9-11.

Example

Consider a five-card trick, where the assistant gets four cards from a deck and is told which card to hide. Moreover, the deck has a duplicate of each card. In the worst case scenario, the assistant gets two duplicates and has to hide the other card. There are six different ways to arrange two pairs of cards. Thus, the assistant can signal a number 1 through 6. The hidden card can't take a value of the cards on the table, so the maximum number of distinct values is 8. Thus a(5) = 8.

Mathematica

Table[(K - 1) !/(2^Floor[(K - 1)/2]) + Floor[(K - 1)/2], {K, 1, 25}]

Crossrefs

Cf. A370888, A371217, A372255.

Sequence in context: A194810 A271216 A102000 * A165904 A192008 A298989

Adjacent sequences: A372253 A372254 A372255 * A372257 A372258 A372259

Keyword

nonn

Author

Tanya Khovanova and the MIT PRIMES STEP junior group, Apr 24 2024

Status

approved