A299591 Number of n X 4 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

5, 5, 11, 23, 53, 121, 250, 533, 1162, 2490, 5327, 11465, 24641, 52882, 113593, 244046, 524134, 1125735, 2418077, 5193785, 11155562, 23961133, 51466258, 110544050, 237437407, 509992017, 1095411137, 2352832034, 5053646321, 10854722326

Offset

1,1

Comments

Column 4 of A299595.

Links

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

Formula

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

Empirical g.f.: x*(5 + x^2 - 8*x^3 - x^4 + 12*x^5 + 6*x^6 - 4*x^7 - 3*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Feb 15 2018

Example

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

Crossrefs

Cf. A299595.

Sequence in context: A301800 A214827 A298955 * A350920 A173316 A242325

Adjacent sequences: A299588 A299589 A299590 * A299592 A299593 A299594

Keyword

nonn

Author

R. H. Hardin, Feb 13 2018

Status

approved