%I #23 Dec 03 2017 12:12:54
%S 1,2,5,10,60,437,2875,36409,704468,14783959,461938624,22488554884,
%T 1378748967395,115759328877461,14408020654986447,2435526103569141336,
%U 559083220302137929773,182904062593977747117174,83283166161035345074485948,52012981990902321891650583747,45449967513840995133445585972949
%N Number of n X n binary matrices with no more than one 1 in any 3 X 3 sub-block.
%H Alois P. Heinz, <a href="/A140304/b140304.txt">Table of n, a(n) for n = 0..23</a>
%H R. J. Mathar, <a href="http://arxiv.org/abs/1609.03964">Tiling n X m rectangles with 1 X 1 and s X s squares</a>, arXiv:1609.03964 [math.CO], 2016.
%t $RecursionLimit = 10^4;
%t b[n_, l_] := b[n, l] = Module[{k, m}, m = Min[l]; Which[n < 3, 1, m > 0, b[n - m, l - m], True, k = 1; While[l[[k]] > 0, k++]; b[n, ReplacePart[l, k -> 1]] + Expand[If[k + 1 < Length[l] && l[[k + 1 ;; k + 2]] == {0, 0}, b[n, ReplacePart[l, {k -> 3, k + 1 -> 3, k + 2 -> 3}]]*x, 0]]]];
%t a[n_] := a[n] = Function[p, Sum[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n + 2, Table[0, n + 2]]];
%t Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 15}] (* _Jean-François Alcover_, Nov 11 2017, after _Alois P. Heinz_ *)
%Y Cf. A139810. Row sums of A276171.
%K nonn
%O 0,2
%A _R. H. Hardin_, May 27 2008
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