A318209 Number of nX3 0..1 arrays with every element unequal to 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 6, 4, 21, 47, 125, 329, 842, 2254, 5893, 15435, 40669, 106859, 280658, 738110, 1940361, 5099669, 13407853, 35248057, 92658886, 243597948, 640404049, 1683558645, 4425986909, 11635671179, 30589415206, 80417882852, 211414206553

Offset

1,2

Comments

Column 3 of A318214.

Links

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

Formula

Empirical: a(n) = a(n-1) +5*a(n-2) +6*a(n-3) -8*a(n-4) -32*a(n-5) -19*a(n-6) +17*a(n-7) +43*a(n-8) +36*a(n-9) +24*a(n-10) +8*a(n-11) -10*a(n-12) -66*a(n-13) -26*a(n-14) +28*a(n-15) +8*a(n-16) -20*a(n-17) -2*a(n-18) +46*a(n-19) -18*a(n-20) -44*a(n-21) +32*a(n-23) -5*a(n-24) -15*a(n-25) +13*a(n-26) +6*a(n-27) -8*a(n-28) -4*a(n-29) +5*a(n-30) +a(n-31) -a(n-32) for n>33

Example

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

Crossrefs

Cf. A318214.

Sequence in context: A321417 A185734 A292696 * A120462 A236602 A169689

Adjacent sequences: A318206 A318207 A318208 * A318210 A318211 A318212

Keyword

nonn

Author

R. H. Hardin, Aug 21 2018

Status

approved