A058053 Number of 3-rowed binary matrices with n ones and no zero columns, up to row and column permutation.

1, 1, 3, 6, 11, 18, 33, 49, 78, 117, 171, 242, 346, 469, 640, 855, 1127, 1463, 1896, 2405, 3045, 3813, 4736, 5831, 7156, 8684, 10507, 12627, 15092, 17935, 21249, 25004, 29341, 34272, 39875, 46207, 53407, 61446, 70528, 80682, 92026, 104650, 118752

Offset

0,3

Comments

Number of 3 x n binary matrices with n ones up to row and column permutation.

Links

Table of n, a(n) for n=0..42.

Vladeta Jovovic, Expansion of generating function.

Formula

a(n)= coefficient of x^n*y^n in expansion of 1 / 3!*(1 / (1 - x) / (1 - x*y)^3 / (1 - x*y^2)^3 / (1 - x*y^3) + 3 / (1 - x) / (1 - x*y) / (1 - x*y^2) / (1 - x*y^3) / (1 - x^2*y^2) / (1 - x^2*y^4) + 2 / (1 - x) / (1 - x*y^3) / (1 - x^3*y^3) / (1 - x^3*y^6)).

Empirical g.f.: -(x^8-x^7+x^6+x^4+x^2-x+1) / ((x-1)^7*(x+1)^3*(x^2-x+1)*(x^2+1)*(x^2+x+1)^3). - Colin Barker, Jul 11 2013

Crossrefs

Cf. A002727, A049311.

Sequence in context: A053992 A052825 A003082 * A264923 A321381 A238903

Adjacent sequences: A058050 A058051 A058052 * A058054 A058055 A058056

Keyword

nonn

Author

Vladeta Jovovic, Nov 19 2000

Extensions

a(21)-a(42) from Max Alekseyev, Jan 21 2010

Status

approved