A006380 Number of equivalence classes of 4 X n binary matrices when one can permute rows, permute columns and complement columns.

1, 3, 8, 19, 41, 81, 153, 273, 468, 774, 1240, 1930, 2933, 4356, 6341, 9064, 12743, 17643, 24093, 32479, 43270, 57019, 74377, 96103, 123089, 156354, 197081, 246622, 306519, 378520, 464614, 567028, 688276, 831169, 998845, 1194793, 1422899, 1687447, 1993182

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• M. A. Harrison, On the number of classes of binary matrices, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)
• Index entries for sequences related to binary matrices
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2,-2,2,5,-8,6,-8,5,2,-2,2,-5,4,-1).
• Index entries for two-way infinite sequences

Crossrefs

Row n=4 of A363349.

Cf. A000601, A006148, A006383.

Programs

Mathematica

LinearRecurrence[{4,-5,2,-2,2,5,-8,6,-8,5,2,-2,2,-5,4,-1},{1,3,8,19,41,81,153,273,468,774,1240,1930,2933,4356,6341,9064},40] (* Harvey P. Dale, Nov 23 2024 *)

PARI

Vec((1 - x + x^2 + x^4 + x^6 - x^7 + x^8)/((1 - x)^8*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2) + O(x^41)) \\ Andrew Howroyd, May 30 2023

Formula

G.f.: (1 - x + x^2 + x^4 + x^6 - x^7 + x^8)/((1 - x)^8*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - Andrew Howroyd, May 30 2023

Extensions

Terms a(7) onwards from Max Alekseyev, Feb 05 2010