A005783 Number of 3-covers of an unlabeled n-set. (Formerly M2790)

1, 3, 9, 23, 51, 103, 196, 348, 590, 960, 1506, 2290, 3393, 4905, 6945, 9651, 13185, 17739, 23542, 30846, 39954, 51206, 64986, 81730, 101935, 126141, 154967, 189093, 229269, 276325, 331182, 394830, 468372, 553002, 650016, 760824, 886963

Offset

0,2

Comments

Equals first differences of A002727. - Vladeta Jovovic, May 24 2000

Number of 3 X n binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

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

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000 (terms for n = 1..1000 from T. D. Noe)

R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.

Masaaki Harada, Ken Saito, Binary linear complementary dual codes, arXiv:1802.06985 [math.CO], 2018.

Vladeta Jovovic, Binary matrices up to row and column permutations

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,-1,3,6,-6,-3,1,3,1,-3,1).

Formula

G.f.: (x^6+x^4+2*x^3+x^2+1)/((1-x^3)^2*(1-x^2)^2*(1-x)^3).

a(n) ~ n^6/4320. - Stefano Spezia, Aug 08 2022

a(n) = n^6/4320 + 7*n^5/1440 + 79*n^4/1728 + 35*n^3/144 + 2939*n^2/4320 + 8863*n/8640 + 1 + (n/16 + 7/32)*floor(n/2) + (n/9 + 11/27)*floor(n/3) + floor((n+1)/3)/27. - Vaclav Kotesovec, Aug 09 2022

Mathematica

CoefficientList[Series[(x^6+x^4+2x^3+x^2+1)/((1-x^3)^2(1-x^2)^2 (1-x)^3), {x, 0, 50}], x] (* Harvey P. Dale, May 19 2011 *)

Prog

(PARI) Vec(G(3, x)*(1 - x) + O(x^40)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023

Crossrefs

Column 3 of A055080.

Cf. A002727, A002620, A005784, A005785, A005786, A055066.

Sequence in context: A146693 A227259 A064551 * A263330 A146440 A244331

Adjacent sequences: A005780 A005781 A005782 * A005784 A005785 A005786

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, May 24 2000

a(0) = 1 prepended by Stefano Spezia, Aug 09 2022

Status

approved