A269431 Number of length-n 0..4 arrays with no repeated value greater than the previous repeated value.

5, 25, 125, 615, 2995, 14455, 69235, 329430, 1558430, 7334806, 34364270, 160340610, 745362730, 3453222850, 15949215754, 73454841775, 337413819915, 1546145183895, 7068979186035, 32251365241137, 146853223312325, 667445619383425

Offset: 1

Author

R. H. Hardin, Feb 26 2016

Keywords

• nonn

Examples

			Some solutions for n=7:
..3. .2. .3. .4. .2. .3. .1. .1. .1. .3. .0. .2. .0. .0. .0. .0
..1. .1. .3. .1. .1. .2. .2. .3. .3. .2. .0. .2. .1. .1. .0. .3
..4. .3. .4. .1. .0. .0. .2. .3. .1. .0. .2. .0. .4. .0. .0. .4
..1. .2. .2. .0. .2. .2. .0. .4. .0. .0. .4. .4. .2. .2. .2. .4
..1. .2. .1. .1. .2. .1. .4. .0. .2. .0. .0. .1. .4. .4. .1. .2
..0. .4. .4. .1. .4. .0. .0. .3. .4. .1. .2. .2. .0. .3. .0. .4
..4. .3. .3. .4. .3. .4. .2. .0. .2. .2. .1. .4. .4. .2. .4. .0
		

Links

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

Crossrefs

Column 4 of A269435.

Formula

Empirical: a(n) = 20*a(n-1) - 155*a(n-2) + 560*a(n-3) - 810*a(n-4) - 136*a(n-5) + 810*a(n-6) + 560*a(n-7) + 155*a(n-8) + 20*a(n-9) + a(n-10).

Empirical g.f.: x*(5 - 75*x + 400*x^2 - 810*x^3 + 120*x^4 + 810*x^5 + 560*x^6 + 155*x^7 + 20*x^8 + x^9) / (1 - 4*x - x^2)^5. - Colin Barker, Jan 21 2019