A269411 Number of length-5 0..n arrays with no repeated value greater than or equal to the previous repeated value.

12, 159, 804, 2670, 6960, 15477, 30744, 56124, 95940, 155595, 241692, 362154, 526344, 745185, 1031280, 1399032, 1864764, 2446839, 3165780, 4044390, 5107872, 6383949, 7902984, 9698100, 11805300, 14263587, 17115084, 20405154, 24182520

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^5 + 5*n^4 + (11/2)*n^3 + n^2 - (1/2)*n.

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

G.f.: 3*x*(4 + 29*x + 10*x^2 - 3*x^3) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Row 5 of A269409.

Sequence in context: A220225 A213376 A269642 * A347748 A226297 A286721

Adjacent sequences: A269408 A269409 A269410 * A269412 A269413 A269414

Keyword

nonn

Author

R. H. Hardin, Feb 25 2016

Status

approved