A306168 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

5, 21, 30, 93, 249, 544, 1372, 3411, 8269, 20472, 50397, 123803, 305272, 751590, 1849735, 4556239, 11219928, 27625541, 68032151, 167535478, 412552316, 1015939459, 2501834023, 6160893450, 15171602577, 37361209577, 92004521524

Offset

1,1

Comments

Column 4 of A306172.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +16*a(n-3) -26*a(n-4) -3*a(n-5) -103*a(n-6) +137*a(n-7) +32*a(n-8) +371*a(n-9) -406*a(n-10) -152*a(n-11) -915*a(n-12) +801*a(n-13) +422*a(n-14) +1710*a(n-15) -1092*a(n-16) -751*a(n-17) -2415*a(n-18) +1006*a(n-19) +977*a(n-20) +2609*a(n-21) -505*a(n-22) -986*a(n-23) -2180*a(n-24) -154*a(n-25) +630*a(n-26) +1281*a(n-27) +325*a(n-28) -267*a(n-29) -512*a(n-30) -276*a(n-31) -13*a(n-32) +49*a(n-33) +74*a(n-34) +52*a(n-35) +32*a(n-36) +11*a(n-37) -7*a(n-38) -6*a(n-39) -3*a(n-40) for n>41

Example

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

Crossrefs

Cf. A306172.

Sequence in context: A316235 A317156 A304665 * A305645 A316921 A316423

Adjacent sequences: A306165 A306166 A306167 * A306169 A306170 A306171

Keyword

nonn

Author

R. H. Hardin, Jun 23 2018

Status

approved