A269410 Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value.

9, 63, 222, 570, 1215, 2289, 3948, 6372, 9765, 14355, 20394, 28158, 37947, 50085, 64920, 82824, 104193, 129447, 159030, 193410, 233079, 278553, 330372, 389100, 455325, 529659, 612738, 705222, 807795, 921165, 1046064, 1183248, 1333497

Offset: 1

Author

R. H. Hardin, Feb 25 2016

Keywords

• nonn

Examples

			Some solutions for n=8:
..8. .3. .1. .0. .3. .0. .8. .2. .3. .1. .0. .4. .3. .5. .4. .6
..8. .8. .3. .5. .4. .2. .1. .4. .0. .5. .2. .4. .0. .6. .4. .8
..4. .7. .3. .8. .7. .2. .0. .5. .3. .3. .7. .0. .0. .1. .2. .0
..0. .8. .8. .7. .5. .8. .5. .8. .2. .8. .0. .0. .2. .1. .4. .2
		

Links

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

Crossrefs

Row 4 of A269409.

Formula

Empirical: a(n) = n^4 + 4*n^3 + (7/2)*n^2 + (1/2)*n.

Conjectures from Colin Barker, Jan 21 2019: (Start)

G.f.: 3*x*(3 + 6*x - x^2) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)