A269682 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

30, 1206, 10700, 57030, 220050, 681254, 1799256, 4215510, 8995310, 17809110, 33159204, 58656806, 99354570, 162139590, 256191920, 393513654, 589533606, 863792630, 1240714620, 1750468230, 2429924354, 3323714406, 4485394440

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 + 8*n^3 + 10*n^2 + 12*n - 10 for n>1.

Conjectures from Colin Barker, Jan 26 2019: (Start)

G.f.: 2*x*(15 + 483*x + 946*x^2 + 1759*x^3 - 1013*x^4 + 617*x^5 - 376*x^6 + 101*x^7 - 12*x^8) / (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>9.

(End)

Example

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

Crossrefs

Row 7 of A269678.

Sequence in context: A265101 A214820 A259462 * A269471 A060076 A174716

Adjacent sequences: A269679 A269680 A269681 * A269683 A269684 A269685

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved