|
|
A213977
|
|
Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 0 0 ].
|
|
2
|
|
|
1, 2, 14, 200, 3536, 67472, 1423168, 34048352, 927156224, 28490354432, 976839578624, 36983803914752, 1532587515049984, 68997562105014272, 3353462146559209472, 175003916852177604608, 9760034505494167420928, 579311442062239341412352, 36462558160899681920745472, 2425761875540844266778656768
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Ju and Seo give an e.g.f. (see PARI code).
|
|
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 *)
|
|
PROG
|
(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))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|