This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372256 #14 May 28 2025 11:11:41
%S A372256 1,1,2,4,8,32,93,633,2524,22684,113405,1247405,7484406,97297206,
%T A372256 681080407,10216206007,81729648008,1389404016008,12504636144009,
%U A372256 237588086736009,2375880867360010,49893498214560010,548828480360160011,12623055048283680011,151476660579404160012
%N A372256 a(n) = (n-1)!/2^floor((n-1)/2) + floor((n-1)/2).
%C A372256 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.
%H A372256 Michael Kleber and Ravi Vakil, <a href="https://web.northeastern.edu/seigen/11Magic/Articles/Best%20Card%20Trick.pdf">The best card trick</a>, The Mathematical Intelligencer 24 (2002), 9-11.
%H A372256 Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, Samuel Tsui, and Tanya Khovanova, <a href="https://arxiv.org/abs/2405.21007">Card Tricks and Information</a>, arXiv:2405.21007 [math.HO], 2024.
%e A372256 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.
%t A372256 Table[(K - 1) !/(2^Floor[(K - 1)/2]) + Floor[(K - 1)/2], {K, 1, 25}]
%Y A372256 Cf. A370888, A371217, A372255.
%K A372256 nonn
%O A372256 1,3
%A A372256 _Tanya Khovanova_ and the MIT PRIMES STEP junior group, Apr 24 2024