A181252 - OEIS

%I #12 Jun 09 2023 22:23:47

%S 512,169209,61986457,22161786304,7969215344753,2861765993703849,

%T 1027999596778673856,369248337357375835969,132633131268024896655873,

%U 47641303155727829675539968,17112587585474467714330327353

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

%C Column 9 of A181253.

%H R. H. Hardin, <a href="/A181252/b181252.txt">Table of n, a(n) for n=1..200</a>

%H Robert Israel, <a href="/A181252/a181252.pdf">Maple-assisted derivation of recurrence</a>

%H Robert Israel, <a href="/A181252/a181252.txt">Linear recurrence of order 48</a>

%F Linear recurrence of order 48: see link. - _Robert Israel_, Apr 02 2020

%p for i from 1 to 512 do Configs[i]:= convert(2^9+i-1,base,2)[1..9] od:

%p Compatible:= proc(i,j)

%p 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 end proc:

%p T:= Matrix(512,512,Compatible):

%p v:= Vector(512,1):

%p TV[0]:= v:

%p for nn from 1 to 23 do TV[nn]:= T . TV[nn-1] od:

%p seq(v^%T . TV[n],n=0..23); # _Robert Israel_, Apr 02 2020

%Y Cf. A181253.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 10 2010