A250382 Number of length n+3 0..3 arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.

156, 432, 1208, 3384, 9480, 26578, 74528, 208998, 586102, 1643650, 4609526, 12927186, 36253772, 101672196, 285136136, 799654742, 2242605598, 6289313722, 17638176794, 49465700416, 138724972590, 389049740574, 1091077541772

Offset

1,1

Comments

Column 3 of A250387.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) -7*a(n-3) +a(n-4) +5*a(n-5) -48*a(n-6) +6*a(n-7) +80*a(n-8) -37*a(n-9) -15*a(n-10) +81*a(n-11) -34*a(n-12) -16*a(n-13) +20*a(n-14) -26*a(n-15) -4*a(n-16) +8*a(n-17).

Empirical g.f.: 2*x*(78 + 60*x - 218*x^2 - 50*x^3 - 230*x^4 - 1029*x^5 + 890*x^6 + 1894*x^7 - 988*x^8 + 285*x^9 + 1852*x^10 - 1178*x^11 - 328*x^12 + 298*x^13 - 788*x^14 - 24*x^15 + 240*x^16) / (1 - 2*x - 5*x^2 + 7*x^3 - x^4 - 5*x^5 + 48*x^6 - 6*x^7 - 80*x^8 + 37*x^9 + 15*x^10 - 81*x^11 + 34*x^12 + 16*x^13 - 20*x^14 + 26*x^15 + 4*x^16 - 8*x^17). - Colin Barker, Aug 20 2017

Example

Some solutions for n=6:
..3....3....2....0....0....0....2....0....3....0....1....0....0....1....2....3
..2....1....2....3....3....2....1....3....3....2....2....2....1....3....1....1
..3....2....3....0....1....3....3....0....1....0....3....0....0....0....3....0
..0....3....3....1....0....0....0....3....0....3....1....2....3....0....1....3
..1....0....0....3....2....0....0....1....0....0....3....1....2....3....3....3
..0....0....0....0....3....2....3....3....2....3....0....2....0....1....0....0
..2....2....2....2....0....1....1....2....2....2....0....0....3....0....0....1
..3....1....1....3....3....3....2....0....0....0....3....2....0....2....1....2
..0....3....2....0....0....1....3....1....0....3....1....1....3....3....2....0

Crossrefs

Sequence in context: A298909 A366172 A156849 * A106056 A259947 A043356

Adjacent sequences: A250379 A250380 A250381 * A250383 A250384 A250385

Keyword

nonn

Author

R. H. Hardin, Nov 20 2014

Status

approved