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A006148 Number of 4 X n binary matrices up to row and column permutations.
(Formerly M3919)
19
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
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)
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
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
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 04 2000
Definition corrected by Max Alekseyev, Feb 05 2010
More terms from Vincenzo Librandi, Oct 13 2015
STATUS
approved

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Last modified March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)