A269608 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one or less.

10, 154, 804, 2692, 7030, 15630, 31024, 56584, 96642, 156610, 243100, 364044, 528814, 748342, 1035240, 1403920, 1870714, 2453994, 3174292, 4054420, 5119590, 6397534, 7918624, 9715992, 11825650, 14286610, 17141004, 20434204, 24214942

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 + 7*n^3 - 4*n^2 + n.

Conjectures from Colin Barker, Jan 25 2019: (Start)

G.f.: 2*x*(5 + 47*x + 15*x^2 - 11*x^3 + 4*x^4) / (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=7:
..2. .3. .4. .7. .7. .4. .6. .7. .1. .2. .6. .4. .1. .2. .4. .5
..6. .2. .7. .5. .3. .3. .4. .7. .4. .1. .0. .6. .5. .4. .2. .6
..1. .5. .1. .4. .6. .1. .5. .5. .2. .0. .7. .4. .3. .0. .0. .1
..4. .0. .7. .2. .4. .4. .4. .1. .7. .6. .1. .4. .6. .4. .4. .7
..7. .3. .5. .5. .4. .7. .3. .3. .2. .2. .1. .2. .6. .1. .2. .0

Crossrefs

Row 5 of A269606.

Sequence in context: A307352 A345348 A349490 * A240196 A048907 A061654

Adjacent sequences: A269605 A269606 A269607 * A269609 A269610 A269611

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved