A281203 Number of n X 6 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

10, 94, 310, 804, 1906, 4248, 9118, 19026, 38916, 78356, 155834, 306840, 599204, 1162074, 2240438, 4297644, 8207494, 15613762, 29601530, 55948952, 105457480, 198283598, 371980528, 696408816, 1301351164, 2427600480, 4521378510

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 6*a(n-4) + 4*a(n-6) + 6*a(n-7) + 3*a(n-8) - 2*a(n-9) - 3*a(n-10) - 2*a(n-11) - a(n-12).

Empirical g.f.: 2*x*(1 + x)*(5 + 32*x + 14*x^2 - 43*x^3 - 55*x^4 - 31*x^5 + x^6 + 28*x^7 + 24*x^8 + 10*x^9 + 3*x^10) / (1 - x - 2*x^2 + x^4 + x^5 + x^6)^2. - Colin Barker, Feb 17 2019

Example

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

Crossrefs

Column 6 of A281205.

Sequence in context: A192902 A192903 A050793 * A369335 A126633 A125422

Adjacent sequences: A281200 A281201 A281202 * A281204 A281205 A281206

Keyword

nonn

Author

R. H. Hardin, Jan 17 2017

Status

approved