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A006381 Number of n X 3 binary matrices under row and column permutations and column complementations.
(Formerly M3313)
5
1, 1, 4, 7, 19, 32, 68, 114, 210, 336, 562, 862, 1349, 1987, 2950, 4201, 5991, 8278, 11422, 15386, 20660, 27218, 35718, 46158, 59401, 75475, 95494, 119545, 149035, 184118, 226562, 276620, 336470, 406490, 489344, 585572, 698397, 828549, 979896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of ways in which to label the vertices of the cube (or faces of the octahedron) with nonnegative integers summing to n, where labelings that differ only by rotation or reflection are considered the same. - Isabel C. Lugo (izzycat(AT)gmail.com), Aug 26 2004

REFERENCES

M. A. Harrison, On the number of classes of binary matrices, IEEE Trans. Computers, 22 (1973), 1048-1051.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..38.

Index entries for sequences related to binary matrices

FORMULA

G.f. : (1/(1 - x^1)^8 + 13/(1 - x^2)^4 + 6/(1 - x^1)^4/(1 - x^2)^2 + 12/(1 - x^4)^2 + 8/(1 - x^1)^2/(1 - x^3)^2 + 8/(1 - x^2)^1/(1 - x^6)^1)/48 = (x^14 - 2*x^13 + 3*x^12 - 2*x^11 + 5*x^10 - 4*x^9 + 7*x^8 - 4*x^7 + 7*x^6 - 4*x^5 + 5*x^4 - 2*x^3 + 3*x^2 - 2*x + 1)/(x^6 - 1)/(x^2 + 1)^2/(x^2 + x + 1)/(x + 1)^3/(x - 1)^7.

EXAMPLE

Representatives of the seven classes of 3 X 3 binary matrices are:

[ 1 1 1 ] [ 1 1 0 ] [ 1 0 1 ] [ 1 0 1 ] [ 0 1 1 ] [ 0 1 1 ] [ 0 1 1 ]

[ 1 1 1 ] [ 1 1 1 ] [ 1 1 0 ] [ 1 1 0 ] [ 1 0 1 ] [ 1 0 0 ] [ 1 0 0 ]

[ 1 1 1 ] [ 1 1 1 ] [ 1 1 1 ] [ 1 1 0 ] [ 1 1 0 ] [ 1 1 1 ] [ 1 0 0 ].

CROSSREFS

Cf. A000601, A005232, A006382, A006380, A002727, A006148.

Sequence in context: A024824 A164265 A174465 * A318099 A274691 A102991

Adjacent sequences:  A006378 A006379 A006380 * A006382 A006383 A006384

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Entry revised by Vladeta Jovovic, Aug 05 2000

Definition corrected by Max Alekseyev, Feb 05 2010

STATUS

approved

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Last modified November 26 08:23 EST 2022. Contains 358354 sequences. (Running on oeis4.)