A280854 Number of n X 3 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

4, 29, 46, 96, 256, 678, 1698, 4358, 11218, 28650, 73354, 188066, 481554, 1233194, 3159018, 8091050, 20722730, 53077762, 135947682, 348198514, 891836994, 2284251018, 5850611770, 14985083066, 38381073050, 98304843826, 251786685106

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-3) - a(n-4) + 2*a(n-6) - 2*a(n-7) for n>9.

Empirical g.f.: x*(4 + 21*x - 12*x^2 - 12*x^3 - 48*x^4 + 11*x^5 - 4*x^6 - 16*x^7 + 12*x^8) / (1 - 2*x - 4*x^3 + x^4 - 2*x^6 + 2*x^7). - Colin Barker, Feb 14 2019

Example

Some solutions for n=4:
..0..0..1. .0..1..1. .0..0..1. .0..1..0. .0..1..2. .0..1..0. .0..0..1
..1..2..1. .0..2..2. .1..2..2. .2..2..1. .2..1..0. .2..1..2. .2..1..2
..0..2..0. .1..1..0. .0..1..0. .1..0..0. .2..0..2. .2..0..2. .2..0..0
..1..1..0. .0..2..2. .0..2..2. .1..2..2. .1..1..2. .1..1..0. .1..1..2

Crossrefs

Column 3 of A280859.

Sequence in context: A278823 A042597 A255635 * A042379 A184301 A192025

Adjacent sequences: A280851 A280852 A280853 * A280855 A280856 A280857

Keyword

nonn

Author

R. H. Hardin, Jan 09 2017

Status

approved