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

Author

Vladeta Jovovic, Nov 19 2000

Keywords

• nonn

Comments

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

Links

• Vladeta Jovovic, Expansion of generating function.

Crossrefs

Cf. A002727, A049311.

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

Extensions

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