A243029 Number of length n+3 0..4 arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..4 introduced in 0..4 order.

13, 43, 162, 672, 2962, 13540, 63221, 298775, 1421589, 6789700, 32497044, 155720725, 746674943, 3581570065, 17183126915, 82447803666, 395624032453, 1898458134570, 9110192964029, 43717837035318, 209793618176126

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 10*a(n-2) + a(n-3) - 21*a(n-4) + 13*a(n-5) + 6*a(n-6) + 27*a(n-7) + 10*a(n-8) + 8*a(n-9).

Empirical g.f.: x*(13 - 48*x - 9*x^2 - 45*x^3 + 108*x^4 + 98*x^5 + 154*x^6 + 63*x^7 + 37*x^8) / ((1 - x - x^3)*(1 - 2*x - x^2 - 2*x^3)*(1 - 4*x - 3*x^2 - 4*x^3)). - Colin Barker, Nov 01 2018

Example

Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....0....1....1....1....0....1....1....1....1....0
..0....2....0....0....2....2....1....1....2....2....1....0....1....0....0....1
..2....0....1....0....1....3....0....2....0....1....0....0....1....1....2....2
..3....2....0....0....2....3....1....3....3....3....2....2....2....1....0....0
..0....2....1....1....0....3....1....1....4....0....2....0....0....2....2....3

Crossrefs

Column 4 of A243033.

Sequence in context: A268256 A243894 A303740 * A243030 A243031 A243032

Adjacent sequences: A243026 A243027 A243028 * A243030 A243031 A243032

Keyword

nonn

Author

R. H. Hardin, May 29 2014

Status

approved