The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000316

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A000316

Two decks each have n kinds of cards, 2 of each kind. The first deck is laid out in order. The second deck is shuffled and laid out next to the first. A match occurs if a card from the second deck is next to a card of the same kind from the first deck. a(n) is the number of ways of achieving no matches.
(history; published version)

#90 by Michael De Vlieger at Sun Mar 26 10:27:45 EDT 2023

STATUS

reviewed

approved

#89 by Michel Marcus at Sun Mar 26 07:18:52 EDT 2023

STATUS

proposed

reviewed

#88 by Eduard I. Vatutin at Sun Mar 26 07:04:21 EDT 2023

STATUS

editing

proposed

#87 by Eduard I. Vatutin at Sun Mar 26 07:04:09 EDT 2023

LINKS

E. I. Vatutin, A. D. Belyshev, N. N. Nikitina, and M. O. Manzuk, <a href="http://evatutin.narod.ru/evatutin_dls_scf_gen.pdf">Use of X-based diagonal fillings and ESODLS CMS schemes for enumeration of main classes of diagonal Latin squares</a>, Telecommunications, 2023, No. 1, pp. 2-16, DOI: 10.31044/1684-2588-2023-0-1-2-16 (in Russian).

STATUS

approved

editing

#86 by OEIS Server at Sun Oct 18 16:03:42 EDT 2020

LINKS

T. D. Noe, <a href="/A000316/b000316_1.txt">Table of n, a(n) for n = 0..100</a>

#85 by N. J. A. Sloane at Sun Oct 18 16:03:42 EDT 2020

STATUS

proposed

approved

Discussion

Sun Oct 18

16:03

OEIS Server: Installed new b-file as b000316.txt.  Old b-file is now b000316_1.txt.

#84 by Wesley Ivan Hurt at Fri Oct 09 16:07:39 EDT 2020

STATUS

editing

proposed

#83 by Wesley Ivan Hurt at Fri Oct 09 16:07:28 EDT 2020

FORMULA

a(n) = n * a(n-1) + n! * 4^n * sum(Sum_{a=0..n} (-1)^a / (a! * 2^a), a=0 to n). (End)

STATUS

proposed

editing

#82 by Michel Marcus at Fri Oct 09 12:47:22 EDT 2020

STATUS

editing

proposed

#81 by Michel Marcus at Fri Oct 09 12:47:08 EDT 2020

FORMULA

a(n) = int_Integral_{x>=0..inf} exp(-x)*(x^2 - 4*x + 2)^n dx. Cf. A000166(n) = int_Integral_{x>=0..inf} exp(-x)*(x - 1)^n dx.

STATUS

proposed

editing