A317121 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.

8, 65, 302, 1597, 8598, 46955, 258241, 1422755, 7843425, 43248130, 238491830, 1315207719, 7253029882, 39998826834, 220584887411, 1216478628291, 6708622719753, 36996640542547, 204028682917674, 1125175254860635

Offset

1,1

Comments

Column 4 of A317125.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Example

Some solutions for n=5
..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..1..1..1. .0..0..0..0
..0..1..0..0. .1..1..1..0. .0..0..1..0. .1..1..1..0. .1..1..0..1
..0..0..0..0. .1..1..1..1. .0..1..1..1. .1..1..1..1. .0..1..1..1
..0..0..1..1. .0..1..1..1. .1..1..1..1. .0..1..0..1. .1..1..1..0
..1..0..1..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..1..1..1

Crossrefs

Cf. A317125.

Sequence in context: A304306 A316205 A305772 * A009373 A305589 A317007

Adjacent sequences: A317118 A317119 A317120 * A317122 A317123 A317124

Keyword

nonn

Author

R. H. Hardin, Jul 21 2018

Status

approved