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Number of 4 X n binary matrices up to row and column permutations.
(Formerly M3919)
19

%I M3919 #51 Feb 28 2023 21:09:53

%S 1,5,22,87,317,1053,3250,9343,25207,64167,155004,357009,787586,

%T 1670643,3419552,6774765,13027340,24372942,44462456,79240762,

%U 138204782,236258358,396409924,653639898,1060379169,1694174350,2668300758,4146300078,6361709115,9644583474

%N Number of 4 X n binary matrices up to row and column permutations.

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

%H Andrew Howroyd, <a href="/A006148/b006148.txt">Table of n, a(n) for n = 0..1000</a>

%H M. A. Harrison, <a href="http://dx.doi.org/10.1109/T-C.1973.223649">On the number of classes of binary matrices</a>, IEEE Trans. Computers, 22 (1973), 1048-1051.

%H M. A. Harrison, <a href="/A000711/a000711.pdf">On the number of classes of binary matrices</a>, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)

%H Vladeta Jovovic, <a href="/A005748/a005748.pdf">Binary matrices up to row and column permutations</a>

%H A. Kerber, <a href="/A002727/a002727.pdf">Experimentelle Mathematik</a>, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 19 (1988), 77-83. [Annotated scanned copy]

%H B. Misek, <a href="http://dml.cz/dmlcz/108444">On the number of classes of strongly equivalent incidence matrices</a>, (Czech with English summary) Casopis Pest. Mat. 89 1964 211-218.

%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (6, -12, 6, 6, -6, 22, -54, 33, -4, 12, 60, -125, 54, -54, 70, 87, -132, 64, -132, 87, 70, -54, 54, -125, 60, 12, -4, 33, -54, 22, -6, 6, 6, -12, 6, -1).

%F G.f.: (x^20 - x^19 + 4*x^18 + 9*x^17 + 23*x^16 + 39*x^15 + 90*x^14 + 131*x^13 + 204*x^12 + 238*x^11 + 252*x^10 + 238*x^9 + 204*x^8 + 131*x^7 + 90*x^6 + 39*x^5 + 23*x^4 + 9*x^3 + 4*x^2 - x + 1)/((1 - x^4)^3*(1 - x^3)^4*(1 - x^2)^3*(1 - x)^6). - _Vladeta Jovovic_, Feb 04 2000

%t CoefficientList[Series[(x^20 - x^19 + 4 x^18 + 9 x^17 + 23 x^16 + 39 x^15 + 90 x^14 + 131 x^13 + 204 x^12 + 238 x^11 + 252 x^10 + 238 x^9 + 204 x^8 + 131 x^7 + 90 x^6 + 39 x^5 + 23 x^4 + 9 x^3 + 4 x^2 - x + 1)/((1 - x^4)^3 (1 - x^3)^4 (1 - x^2)^3 (1 - x)^6), {x, 0, 45}], x] (* _Vincenzo Librandi_, Oct 13 2015 *)

%t LinearRecurrence[{6,-12,6,6,-6,22,-54,33,-4,12,60,-125,54,-54,70,87,-132,64,-132,87,70,-54,54,-125,60,12,-4,33,-54,22,-6,6,6,-12,6,-1},{1,5,22,87,317,1053,3250,9343,25207,64167,155004,357009,787586,1670643,3419552,6774765,13027340,24372942,44462456,79240762,138204782,236258358,396409924,653639898,1060379169,1694174350,2668300758,4146300078,6361709115,9644583474,14456861538,21439125178,31471971903,45755970759,65915132560,94129925265},30] (* _Harvey P. Dale_, Jun 22 2021 *)

%o (PARI) Vec(G(4, x) + O(x^40)) \\ G defined in A028657. - _Andrew Howroyd_, Feb 28 2023

%Y Cf. A002623, A002727, A006380.

%Y A diagonal of the array A(m,n) described in A028657. - _N. J. A. Sloane_, Sep 01 2013

%K nonn,nice,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Feb 04 2000

%E Definition corrected by _Max Alekseyev_, Feb 05 2010

%E More terms from _Vincenzo Librandi_, Oct 13 2015