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A189698 Number of 5Xn binary arrays without the pattern 0 0 1 diagonally, vertically or antidiagonally.

%I A189698 #7 Jul 22 2025 11:53:35
%S A189698 20,400,5172,65297,862652,11451149,151788273,2010430729,26638642226,
%T A189698 353018801580,4678246752829,61995665582140,821565095555503,
%U A189698 10887399620742611,144280214103179733,1912006322548221320
%N A189698 Number of 5Xn binary arrays without the pattern 0 0 1 diagonally, vertically or antidiagonally.
%C A189698 Row 5 of A189696
%H A189698 R. H. Hardin, <a href="/A189698/b189698.txt">Table of n, a(n) for n = 1..200</a>
%F A189698 Empirical: a(n) = 20*a(n-1) -60*a(n-2) -633*a(n-3) +4289*a(n-4) -19321*a(n-5) +45093*a(n-6) +478124*a(n-7) -2450407*a(n-8) +3842305*a(n-9) -5871294*a(n-10) -109929744*a(n-11) +546273704*a(n-12) +220749058*a(n-13) -3057836472*a(n-14) +4168921034*a(n-15) -11914638925*a(n-16) -14152632954*a(n-17) +115745535531*a(n-18) -51347303247*a(n-19) +2966824602*a(n-20) +207246843786*a(n-21) -1457083257908*a(n-22) +128501680584*a(n-23) +1854676590096*a(n-24) -844352601056*a(n-25) +5479925969392*a(n-26) +1148855458112*a(n-27) -10789933618176*a(n-28) -902145093976*a(n-29) -5459853101552*a(n-30) -3627163886960*a(n-31) +18812592077712*a(n-32) +8566261898624*a(n-33) -1211282099328*a(n-34) -1296831985536*a(n-35) -12299160022784*a(n-36) -6520706736128*a(n-37) +3578172086272*a(n-38) +2696006297600*a(n-39) +2021760851968*a(n-40) +843021844480*a(n-41) -530584764416*a(n-42) -302591115264*a(n-43) -113839702016*a(n-44) -44088426496*a(n-45) +14579400704*a(n-46) +2214592512*a(n-47) for n>48
%e A189698 Some solutions for 5X3
%e A189698 ..1..0..1....1..1..0....1..1..1....0..0..0....0..1..1....1..1..1....0..1..1
%e A189698 ..1..1..0....1..1..0....1..0..1....1..1..1....1..1..0....1..0..1....1..0..1
%e A189698 ..0..0..1....0..1..0....1..0..1....1..1..0....1..1..0....0..1..1....0..1..0
%e A189698 ..0..1..0....0..0..0....0..0..1....1..0..0....0..1..0....0..1..1....0..1..0
%e A189698 ..0..0..1....0..1..0....1..0..1....0..1..0....0..0..0....0..1..0....0..1..0
%K A189698 nonn
%O A189698 1,1
%A A189698 _R. H. Hardin_ Apr 25 2011