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A006381
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Number of n X 3 binary matrices under row and column permutations and column complementations.
(Formerly M3313)
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5
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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; internal format)
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OFFSET
| 0,3
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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
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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).
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LINKS
| Index entries for sequences related to binary matrices
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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.
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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 ].
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CROSSREFS
| Cf. A000601, A005232, A006382, A006380, A002727, A006148.
Sequence in context: A024824 A164265 A174465 * A102991 A062306 A140167
Adjacent sequences: A006378 A006379 A006380 * A006382 A006383 A006384
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Entry revised by Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 05 2000
Definition corrected by Max Alekseyev (maxale(AT)gmail.com), Feb 05 2010
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