A269541 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than one.

30, 1048, 10192, 55836, 217714, 677200, 1792788, 4205812, 8981446, 17790024, 33133720, 58623628, 99312282, 162086656, 256126684, 393434340, 589438318, 863679352, 1240581216, 1750312444, 2429743810, 3323506608, 4485156772

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 12*n^3 + 22*n^2 - 18*n + 4.

Conjectures from Colin Barker, Jan 24 2019: (Start)

G.f.: 2*x*(15 + 404*x + 1324*x^2 + 982*x^3 - 93*x^4 - 88*x^5 - 22*x^6 - 2*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 7 of A269537.

Sequence in context: A160313 A001821 A027488 * A280216 A075187 A265101

Adjacent sequences: A269538 A269539 A269540 * A269542 A269543 A269544

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved