cp's OEIS Frontend

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

%I A213977 #24 Jul 22 2018 10:42:33
%S A213977 1,2,14,200,3536,67472,1423168,34048352,927156224,28490354432,
%T A213977 976839578624,36983803914752,1532587515049984,68997562105014272,
%U A213977 3353462146559209472,175003916852177604608,9760034505494167420928,579311442062239341412352,36462558160899681920745472,2425761875540844266778656768
%N A213977 Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 0 0 ].
%H A213977 Joerg Arndt, <a href="/A213977/b213977.txt">Table of n, a(n) for n = 0..100</a>
%H A213977 Hyeong-Kwan Ju, Seunghyun Seo, <a href="http://arxiv.org/abs/1107.1299">Enumeration of 0/1-matrices avoiding some 2x2 matrices</a>, arXiv:1107.1299 [math.CO], 2011.
%H A213977 H.-K. Ju and S. Seo, <a href="https://doi.org/10.1016/j.disc.2012.04.019">Enumeration of (0,1)-matrices avoiding some 2 X 2 matrices</a>, Discrete Math., 312 (2012), 2473-2481.
%F A213977 Ju and Seo give an e.g.f. (see PARI code).
%t A213977 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_ *)
%o A213977 (PARI)
%o A213977 N=66; x='x+O('x^N);
%o A213977 W(x)=sum(n=1,N, (-n)^(n-1)*x^n/n! );
%o A213977 w=W(-x*exp(x));
%o A213977 egf=-2*w/(x*(1+w)) + (x^2-1)*exp(2*x)-2*x*(x+1)*exp(4*x);
%o A213977 Vec(serlaplace(egf))
%o A213977 /* _Joerg Arndt_, Jul 19 2012 */
%Y A213977 Cf. A048163, A014235.
%K A213977 nonn
%O A213977 0,2
%A A213977 _N. J. A. Sloane_, Jul 05 2012
%E A213977 More terms from _Joerg Arndt_, Jul 19 2012