cp's OEIS Frontend

A006382 Number of n X 4 binary matrices under row and column permutations and column complementations.

%I A006382 M3814 #26 Mar 07 2025 12:00:31
%S A006382 1,1,5,11,41,101,301,757,1981,4714,11133,24763,53818,111941,226857,
%T A006382 444260,848620,1576226,2862426,5077454,8827758,15043096,25183794,
%U A006382 41434222,67108437,107051463,168402958,261384026,400684767,606936536
%N A006382 Number of n X 4 binary matrices under row and column permutations and column complementations.
%D A006382 M. A. Harrison, On the number of classes of binary matrices, IEEE Trans. Computers, 22 (1973), 1048-1051.
%D A006382 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006382 Andrew Howroyd, <a href="/A006382/b006382.txt">Table of n, a(n) for n = 0..1000</a>
%H A006382 <a href="/index/Rec#order_52">Index entries for linear recurrences with constant coefficients</a>, signature (6, -13, 10, 4, -14, 25, -46, 53, -36, 8, 44, -111, 138, -123, 106, -54, -66, 181, -238, 259, -220, 98, 36, -150, 280, -352, 280, -150, 36, 98, -220, 259, -238, 181, -66, -54, 106, -123, 138, -111, 44, 8, -36, 53, -46, 25, -14, 4, 10, -13, 6, -1).
%H A006382 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%H A006382 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%F A006382 G.f. : (1/(1 - x^1)^16 + 51/(1 - x^2)^8 + 12/(1 - x^1)^8/(1 - x^2)^4 + 84/(1 - x^4)^4 + 12/(1 - x^1 )^4/(1 - x^2)^6 + 32/(1 - x^1)^4/(1 - x^3)^4 + 96/(1 - x^2)^2/(1 - x^6)^2 + 48/(1 - x^1)^2/(1 - x^2)^1/(1 - x^4)^3 + 48/(1 - x^8)^2)/384.
%e A006382 Representatives of the five classes of 2 X 4 binary matrices are:
%e A006382 [ 1 1 1 1 ] [ 1 1 1 0 ] [ 1 1 0 1 ] [ 1 0 1 1 ] [ 0 1 1 1 ]
%e A006382 [ 1 1 1 1 ] [ 1 1 1 1 ] [ 1 1 1 0 ] [ 1 1 0 0 ] [ 1 0 0 0 ]
%Y A006382 Column k=4 of A363349.
%Y A006382 Cf. A005232, A006380, A006381, A002727, A006148.
%K A006382 nonn
%O A006382 0,3
%A A006382 _N. J. A. Sloane_
%E A006382 Entry revised by _Vladeta Jovovic_, Aug 05 2000