A318086 Number of nX3 0..1 arrays with every element unequal to 0, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 7, 7, 11, 15, 62, 104, 141, 275, 741, 1325, 2194, 4346, 9703, 17959, 32463, 64123, 132534, 250208, 470401, 923631, 1843613, 3523413, 6742322, 13174390, 25884507, 49819771, 96089259, 187177999, 365170718, 705571836, 1365582829

Offset

1,2

Comments

Column 3 of A318091.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +4*a(n-4) -12*a(n-5) +7*a(n-6) -12*a(n-7) +20*a(n-8) -6*a(n-9) +13*a(n-10) +10*a(n-11) -19*a(n-12) -2*a(n-13) -26*a(n-14) +26*a(n-15) -4*a(n-16) +10*a(n-17) -10*a(n-18) -2*a(n-19) -a(n-20) +a(n-22) +a(n-24)

Example

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

Crossrefs

Cf. A318091.

Sequence in context: A021443 A045923 A306238 * A244049 A271229 A199886

Adjacent sequences: A318083 A318084 A318085 * A318087 A318088 A318089

Keyword

nonn

Author

R. H. Hardin, Aug 16 2018

Status

approved