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%I #8 Jul 19 2023 10:17:05
%S 776,3264,17116,81308,369152,1719383,7994866,36814964,169690932,
%T 782928672,3607748374,16618930336,76567343262,352730598652,
%U 1624800857183,7484393222731,34475664616145,158804587990863,731493751662765
%N Number of (n+2)X5 binary arrays avoiding patterns 001 and 010 in rows, columns and nw-to-se diagonals.
%H R. H. Hardin, <a href="/A202893/b202893.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) -20*a(n-2) +107*a(n-3) -398*a(n-4) +738*a(n-5) -2666*a(n-6) +6567*a(n-7) -5696*a(n-8) +23763*a(n-9) -38174*a(n-10) -28818*a(n-11) -128857*a(n-12) +91998*a(n-13) +497173*a(n-14) +980615*a(n-15) +2613*a(n-16) -2944178*a(n-17) -6692446*a(n-18) -3201580*a(n-19) +12324831*a(n-20) +31942303*a(n-21) +27028612*a(n-22) -33117909*a(n-23) -116041590*a(n-24) -124565023*a(n-25) +41055880*a(n-26) +313353070*a(n-27) +407261622*a(n-28) +54971014*a(n-29) -612525762*a(n-30) -981333878*a(n-31) -429317040*a(n-32) +851543798*a(n-33) +1753792532*a(n-34) +1184415382*a(n-35) -726958892*a(n-36) -2352756541*a(n-37) -2083099763*a(n-38) +90662131*a(n-39) +2318885002*a(n-40) +2613663583*a(n-41) +745650465*a(n-42) -1576402440*a(n-43) -2392059010*a(n-44) -1253899240*a(n-45) +596726635*a(n-46) +1575476433*a(n-47) +1177422401*a(n-48) +75440229*a(n-49) -705283171*a(n-50) -737641009*a(n-51) -273495008*a(n-52) +169039353*a(n-53) +312071492*a(n-54) +197384459*a(n-55) +18468996*a(n-56) -80302791*a(n-57) -82414262*a(n-58) -34856020*a(n-59) +5887432*a(n-60) +20946985*a(n-61) +15251291*a(n-62) +4417667*a(n-63) -2598284*a(n-64) -3750121*a(n-65) -2034951*a(n-66) -220817*a(n-67) +543926*a(n-68) +447516*a(n-69) +154787*a(n-70) -34294*a(n-71) -59123*a(n-72) -29828*a(n-73) -1394*a(n-74) +4423*a(n-75) +3179*a(n-76) +350*a(n-77) -182*a(n-78) -169*a(n-79) -23*a(n-80) +5*a(n-81) +4*a(n-82).
%e Some solutions for n=3
%e ..1..1..1..1..1....1..1..1..1..1....1..1..1..0..1....1..1..1..1..0
%e ..0..1..1..1..0....1..0..1..1..0....1..0..1..1..0....1..1..0..1..1
%e ..1..1..1..0..0....1..1..1..0..1....1..1..1..1..0....1..1..1..1..1
%e ..1..0..1..1..0....1..1..1..1..1....1..1..1..1..0....0..1..1..1..1
%e ..0..1..1..1..0....0..1..1..1..0....1..0..1..1..0....1..1..1..0..0
%Y Column 3 of A202898
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 25 2011