A266365 Number of possible plugboard settings for a WWII German Enigma Cipher Machine with n cables.

1, 325, 44850, 3453450, 164038875, 5019589575, 100391791500, 1305093289500, 10767019638375, 53835098191875, 150738274937250, 205552193096250, 102776096548125, 7905853580625, 0, 0, 0

Offset

0,2

Comments

a(n) increases to a maximum at n = 11, then decreases.

References

Andrew Hodges, Alan Turing: the Enigma, Princeton University Press, 2014.

Links

Table of n, a(n) for n=0..16.

A. Ray Miller, The Cryptographic Mathematics of Enigma, Cryptologia, 19 (1995), 65-80.

Kalika Prasad and Munesh Kumari, A review on mathematical strength and analysis of Enigma, arXiv:2004.09982 [cs.CR], 2020.

Tony Sale, Counting the Possible Plugboard Setting, Codes and Ciphers, Enigma.

Formula

a(n) = 26! / ((26 - 2n)! n! 2^n) = C(2,26,n) (see A181386).

Mathematica

Table[26!/((26 - 2 n)! n! 2^n), {n, 0, 16}]

Crossrefs

Cf. A181386.

Sequence in context: A374257 A145414 A298106 * A340462 A166220 A121000

Adjacent sequences: A266362 A266363 A266364 * A266366 A266367 A266368

Keyword

nonn

Author

Jonathan Sondow, Dec 28 2015

Status

approved