A280550 Number of n X 4 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 34, 144, 382, 832, 1666, 3182, 5886, 10680, 19122, 33920, 59754, 104690, 182598, 317264, 549398, 948528, 1633186, 2805094, 4807006, 8220440, 14030634, 23904656, 40659818, 69051850, 117099910, 198312144, 335420782, 566645728, 956190466

Offset

1,2

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9) for n>11.

Empirical g.f.: x*(1 + 28*x - 48*x^2 - 79*x^3 + 86*x^4 + 142*x^5 - 57*x^6 - 134*x^7 + 46*x^8 + 39*x^9 - 36*x^10) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019

Example

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

Crossrefs

Column 4 of A280554.

Sequence in context: A158062 A141127 A153465 * A105714 A072319 A031398

Adjacent sequences: A280547 A280548 A280549 * A280551 A280552 A280553

Keyword

nonn

Author

R. H. Hardin, Jan 05 2017

Status

approved