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A181252 Number of n X 9 binary matrices with no 2 X 2 block having four 1's.

%I A181252 #12 Jun 09 2023 22:23:47
%S A181252 512,169209,61986457,22161786304,7969215344753,2861765993703849,
%T A181252 1027999596778673856,369248337357375835969,132633131268024896655873,
%U A181252 47641303155727829675539968,17112587585474467714330327353
%N A181252 Number of n X 9 binary matrices with no 2 X 2 block having four 1's.
%C A181252 Column 9 of A181253.
%H A181252 R. H. Hardin, <a href="/A181252/b181252.txt">Table of n, a(n) for n=1..200</a>
%H A181252 Robert Israel, <a href="/A181252/a181252.pdf">Maple-assisted derivation of recurrence</a>
%H A181252 Robert Israel, <a href="/A181252/a181252.txt">Linear recurrence of order 48</a>
%F A181252 Linear recurrence of order 48: see link. - _Robert Israel_, Apr 02 2020
%p A181252 for i from 1 to 512 do Configs[i]:= convert(2^9+i-1,base,2)[1..9] od:
%p A181252 Compatible:= proc(i,j)
%p A181252 if `and`(seq(evalb(Configs[i][k] + Configs[i][k+1] + Configs[j][k]+Configs[j][k+1] < 4), k=1..8)) then 1 else 0 fi
%p A181252 end proc:
%p A181252 T:= Matrix(512,512,Compatible):
%p A181252 v:= Vector(512,1):
%p A181252 TV[0]:= v:
%p A181252 for nn from 1 to 23 do TV[nn]:= T . TV[nn-1] od:
%p A181252 seq(v^%T . TV[n],n=0..23); # _Robert Israel_, Apr 02 2020
%Y A181252 Cf. A181253.
%K A181252 nonn
%O A181252 1,1
%A A181252 _R. H. Hardin_, Oct 10 2010