A005783 Number of 3-covers of an unlabeled n-set.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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).

Crossrefs

Column 3 of A055080.

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

Programs

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 *)

PARI

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

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

Extensions

More terms from Vladeta Jovovic, May 24 2000

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