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 A202194 Number of (n+2)X(n+2) binary arrays avoiding patterns 001 and 101 in rows and columns 1
 108, 640, 3500, 18144, 90552, 439296, 2084940, 9724000, 44710952, 203164416, 914004728, 4077035200, 18052470000, 79420170240, 347424465420, 1512176830560, 6552247686600, 28276211040000, 121580638419240, 521033622457920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Diagonal of A202202 LINKS R. H. Hardin, Table of n, a(n) for n = 1..21 FORMULA Empirical: (n+1)*a(n) -2*(3n+4)*a(n-1) +4*(3n-2)*a(n-2) +8*(3-2n)*a(n-3)=0. - R. J. Mathar, Dec 14 2011 Conjecture: a(n) = 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!). - Michael Somos, Sep 11 2020 EXAMPLE Some solutions for n=3 ..0..1..1..0..0....1..1..0..0..0....0..1..1..1..1....0..1..1..1..0 ..1..1..1..1..1....0..1..1..1..0....1..1..1..1..1....1..1..1..1..1 ..0..1..1..1..1....0..1..1..0..0....1..1..1..1..1....0..1..1..1..0 ..0..1..0..0..0....0..1..1..0..0....1..1..1..0..0....0..1..0..0..0 ..0..1..0..0..0....0..1..0..0..0....1..1..0..0..0....0..0..0..0..0 PROG (PARI) {a(n) = if(n<1, 0, 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!))}; /* Michael Somos, Sep 11 2020 */ CROSSREFS Sequence in context: A129027 A288706 A204276 * A333757 A203373 A292343 Adjacent sequences:  A202191 A202192 A202193 * A202195 A202196 A202197 KEYWORD nonn AUTHOR R. H. Hardin Dec 14 2011 STATUS approved

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Last modified July 24 09:52 EDT 2021. Contains 346273 sequences. (Running on oeis4.)