A267228 Number of length-n 0..4 arrays with no following elements greater than or equal to the first repeated value.

5, 25, 110, 470, 1980, 8274, 34396, 142474, 588596, 2426738, 9989292, 41065818, 168636772, 691859842, 2836150748, 11617837802, 47559474708, 194575978386, 795613053964, 3251559375226, 13282278193604, 54232112235170

Offset: 1

Author

R. H. Hardin, Jan 12 2016

Keywords

• nonn

Comments

Column 4 of A267232.

Examples

			Some solutions for n=6:
..1....0....0....4....0....4....1....2....2....0....1....1....2....3....1....3
..4....4....3....2....1....4....2....3....0....2....3....4....0....1....3....1
..3....2....2....3....0....0....0....2....1....2....2....1....3....4....0....2
..0....4....3....1....4....3....1....0....2....1....1....3....4....0....2....3
..4....0....2....0....2....3....4....4....4....0....3....1....2....3....0....0
..2....2....2....0....1....0....0....3....1....0....1....3....3....3....3....4
		

Links

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

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 14*a(n-1) -75*a(n-2) +190*a(n-3) -224*a(n-4) +96*a(n-5) for n>6.

Conjectures from Colin Barker, Feb 05 2018: (Start)

G.f.: x*(5 - 45*x + 135*x^2 - 145*x^3 + 20*x^4 + 24*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2).

a(n) = (2*(-3*2^(1+n) - 8*3^n + 41*4^n - 8) + 3*4^n*n) / 48 for n>1.

(End)