The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A325015 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A325015

Array read by descending antidiagonals: T(n,k) is the number of achiral colorings of the facets of a regular n-dimensional orthoplex using up to k colors.
(history; published version)

#26 by Michel Marcus at Thu Aug 27 04:32:18 EDT 2020

STATUS

reviewed

approved

#25 by Joerg Arndt at Thu Aug 27 01:51:25 EDT 2020

STATUS

proposed

reviewed

#24 by Michel Marcus at Wed Aug 26 16:44:26 EDT 2020

STATUS

editing

proposed

#23 by Michel Marcus at Wed Aug 26 16:44:01 EDT 2020

NAME

Array read by descending antidiagonals: AT(n,k) is the number of achiral colorings of the facets of a regular n-dimensional orthoplex using up to k colors.

FORMULA

AT(n,k) = 2*A325013(n,k) - A325012(n,k) = A325012(n,k) - 2*A325014(n,k) = A325013(n,k) - A325014(n,k).

AT(n,k) = Sum_{j=1..3*2^(n-2)} A325019(n,j) * binomial(k,j).

EXAMPLE

Array begins with AT(1,1):

...

For AT(2,2)=6, two squares have all edges the same color, two have three edges the same color, one has opposite edges the same color, and one has opposite edges different colors.

STATUS

proposed

editing

Discussion

Wed Aug 26

16:44

Michel Marcus: rather T(n,k) than A(n,k)

#22 by Michel Marcus at Wed Aug 26 16:31:02 EDT 2020

STATUS

editing

proposed

#21 by Michel Marcus at Wed Aug 26 16:30:53 EDT 2020

LINKS

E. M. Palmer and R. W. Robinson, <a href="https://projecteucliddoi.org/euclid10.acta1007/1485889789BF02392038">Enumeration under two representations of the wreath product</a>, Acta Math., 131 (1973), 123-143.

STATUS

proposed

editing

Discussion

Wed Aug 26

16:31

Michel Marcus: with doi link

#20 by Robert A. Russell at Wed Aug 26 16:16:42 EDT 2020

STATUS

editing

proposed

#19 by Robert A. Russell at Wed Aug 26 16:16:02 EDT 2020

FORMULA

A(n,k) = (2*A325013(n,k) - A325012(n,k)) / 2 = A325012(n,k) - 2*A325014(n,k) = A325013(n,k) - A325014(n,k).

STATUS

approved

editing

#18 by Alois P. Heinz at Sat Jun 15 14:43:55 EDT 2019

STATUS

proposed

approved

#17 by Robert A. Russell at Sat Jun 15 13:23:59 EDT 2019

STATUS

editing

proposed