A213977 Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 0 0 ].

1, 2, 14, 200, 3536, 67472, 1423168, 34048352, 927156224, 28490354432, 976839578624, 36983803914752, 1532587515049984, 68997562105014272, 3353462146559209472, 175003916852177604608, 9760034505494167420928, 579311442062239341412352, 36462558160899681920745472, 2425761875540844266778656768

Offset: 0

Author

N. J. A. Sloane, Jul 05 2012

Keywords

• nonn

Links

• Joerg Arndt, Table of n, a(n) for n = 0..100
• Hyeong-Kwan Ju, Seunghyun Seo, Enumeration of 0/1-matrices avoiding some 2x2 matrices, arXiv:1107.1299 [math.CO], 2011.
• H.-K. Ju and S. Seo, Enumeration of (0,1)-matrices avoiding some 2 X 2 matrices, Discrete Math., 312 (2012), 2473-2481.

Crossrefs

Cf. A048163, A014235.

Programs

Mathematica

terms = 20; w = ProductLog[-x E^x]; CoefficientList[-2w/(x(w+1)) + (x^2-1) E^(2x) - 2x(x+1) E^(4x) + O[x]^terms, x]*Range[0, terms-1]! (* Jean-François Alcover, Jul 22 2018, after Joerg Arndt *)

PARI

N=66; x='x+O('x^N);
W(x)=sum(n=1,N, (-n)^(n-1)*x^n/n! );
w=W(-x*exp(x));
egf=-2*w/(x*(1+w)) + (x^2-1)*exp(2*x)-2*x*(x+1)*exp(4*x);
Vec(serlaplace(egf))
/* Joerg Arndt, Jul 19 2012 */

Formula

Ju and Seo give an e.g.f. (see PARI code).

Extensions

More terms from Joerg Arndt, Jul 19 2012