A317121 - OEIS

%I #4 Jul 21 2018 17:31:26

%S 8,65,302,1597,8598,46955,258241,1422755,7843425,43248130,238491830,

%T 1315207719,7253029882,39998826834,220584887411,1216478628291,

%U 6708622719753,36996640542547,204028682917674,1125175254860635

%N Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A317125.

%H R. H. Hardin, <a href="/A317121/b317121.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +a(n-2) +2*a(n-3) -120*a(n-4) -77*a(n-5) +152*a(n-6) +845*a(n-7) +1338*a(n-8) -940*a(n-9) -3462*a(n-10) -6115*a(n-11) +2228*a(n-12) +7367*a(n-13) +7789*a(n-14) -15611*a(n-15) -47569*a(n-16) -12276*a(n-17) +66994*a(n-18) +205581*a(n-19) +256386*a(n-20) +170683*a(n-21) -118420*a(n-22) -434392*a(n-23) -849661*a(n-24) -1153016*a(n-25) -1031924*a(n-26) -405784*a(n-27) +556041*a(n-28) +1433151*a(n-29) +2167330*a(n-30) +2311351*a(n-31) +1780070*a(n-32) +1357492*a(n-33) -46688*a(n-34) -880318*a(n-35) -1199783*a(n-36) -1327002*a(n-37) -1109295*a(n-38) -493500*a(n-39) -152390*a(n-40) +149838*a(n-41) +363761*a(n-42) +193613*a(n-43) +130356*a(n-44) +33207*a(n-45) -54237*a(n-46) -68686*a(n-47) -54274*a(n-48) -19271*a(n-49) -4727*a(n-50) +4292*a(n-51) +4741*a(n-52) +2108*a(n-53) +2116*a(n-54) +712*a(n-55) +320*a(n-56) +96*a(n-57) for n>59

%e Some solutions for n=5

%e ..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..1..1..1. .0..0..0..0

%e ..0..1..0..0. .1..1..1..0. .0..0..1..0. .1..1..1..0. .1..1..0..1

%e ..0..0..0..0. .1..1..1..1. .0..1..1..1. .1..1..1..1. .0..1..1..1

%e ..0..0..1..1. .0..1..1..1. .1..1..1..1. .0..1..0..1. .1..1..1..0

%e ..1..0..1..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..1..1..1

%Y Cf. A317125.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 21 2018