A269436 Number of length-4 0..n arrays with no repeated value greater than the previous repeated value.

15, 78, 250, 615, 1281, 2380, 4068, 6525, 9955, 14586, 20670, 28483, 38325, 50520, 65416, 83385, 104823, 130150, 159810, 194271, 234025, 279588, 331500, 390325, 456651, 531090, 614278, 706875, 809565, 923056, 1048080, 1185393, 1335775

Offset: 1

Author

R. H. Hardin, Feb 26 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A269435.

Formula

Empirical: a(n) = n^4 + 4*n^3 + (11/2)*n^2 + (7/2)*n + 1.

Conjectures from Colin Barker, Jan 22 2019: (Start)

G.f.: x*(15 + 3*x + 10*x^2 - 5*x^3 + x^4) / (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)