A006148 - OEIS

A006148

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

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

M. A. Harrison, On the number of classes of binary matrices, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)

Vladeta Jovovic, Binary matrices up to row and column permutations

A. Kerber, Experimentelle Mathematik, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 19 (1988), 77-83. [Annotated scanned copy]

B. Misek, On the number of classes of strongly equivalent incidence matrices, (Czech with English summary) Casopis Pest. Mat. 89 1964 211-218.

Index entries for linear recurrences with constant coefficients, 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).

FORMULA

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

MATHEMATICA

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 *)

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 *)

PROG

(PARI) Vec(G(4, x) + O(x^40)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023

CROSSREFS

Cf. A002623, A002727, A006380.

A diagonal of the array A(m,n) described in A028657. - N. J. A. Sloane, Sep 01 2013

Sequence in context: A216041 A122058 A191008 * A262293 A086090 A037529

Adjacent sequences: A006145 A006146 A006147 * A006149 A006150 A006151

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS