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
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, May 24 2000
a(0) = 1 prepended by Stefano Spezia, Aug 09 2022
STATUS
approved