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 A372265 #15 Jun 06 2024 12:45:22
%S A372265 0,2,4,7,14,31,76,207,609,1913,6327,21896,78922,295272,1143549,
%T A372265 4574158,18859692,80014850,348776594,1559776287,7147792837,
%U A372265 33526120102,160785623566,787685471345,3938427356638,20082117944270,104349745809099,552166953567254,2973510046012938,16286585271694984
%N A372265 a(n) = floor((2*n - 3 + sqrt(1 + 4*n!))/2).
%C A372265 Information-theoretic bound on the largest card deck with which one can perform an n-card trick, when the assistant chooses two cards to hide.
%C A372265 The bound is based on the following argument: The assistant has n choose 2 ways to pick the hidden cards and (n-2)! ways to arrange the rest of the cards. The number of strategies can't be smaller than the number of potential guesses by the magician which is d - n + 2 choose 2, where d is the deck size.
%H A372265 Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, <a href="https://arxiv.org/abs/2405.21007">Card Tricks and Information</a>, arXiv:2405.21007 [math.HO], 2024. See p. 21.
%H A372265 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.
%e A372265 For n=3, the equation on the deck size becomes the following: d-1 choose 2 can't exceed 3. Thus, a(3) = 4.
%t A372265 Table[Floor[(2 n - 3 + Sqrt[1 + 4 n!])/2], {n, 30}]
%Y A372265 Cf. A370888, A371217, A372255, A372256, A372264.
%K A372265 nonn
%O A372265 1,2
%A A372265 _Tanya Khovanova_ and the MIT PRIMES STEP junior group, Apr 24 2024