A269691 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by plus or minus one modulo n+1.

24, 201, 944, 2995, 7584, 16541, 32416, 58599, 99440, 160369, 248016, 370331, 536704, 758085, 1047104, 1418191, 1887696, 2474009, 3197680, 4081539, 5150816, 6433261, 7959264, 9761975, 11877424, 14344641, 17205776, 20506219, 24294720

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 + 10*n^3 + 4*n^2 - 3*n - 1 for n>1.

Conjectures from Colin Barker, Jan 28 2019: (Start)

G.f.: x*(24 + 57*x + 98*x^2 - 134*x^3 + 114*x^4 - 47*x^5 + 8*x^6) / (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>7.

(End)

Example

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

Crossrefs

Row 5 of A269690.

Sequence in context: A055857 A239574 A223748 * A282644 A283540 A047659

Adjacent sequences: A269688 A269689 A269690 * A269692 A269693 A269694

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved