A268948 Number of length-7 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

30, 969, 9684, 54045, 213042, 667065, 1773384, 4171869, 8925990, 17704137, 33006300, 58441149, 99058554, 161742585, 255670032, 392839485, 588676014, 862716489, 1239380580, 1748832477, 2427938370, 3321324729, 4482542424

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 + 10*n^4 + 4*n^3 + n^2 + 4*n - 3.

Conjectures from Colin Barker, Jan 17 2019: (Start)

G.f.: 3*x*(10 + 243*x + 924*x^2 + 675*x^3 - 110*x^4 - 55*x^5 - 8*x^6 + 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=4:
..4. .2. .4. .3. .1. .1. .2. .0. .1. .4. .4. .2. .4. .2. .3. .3
..1. .0. .0. .1. .3. .0. .0. .1. .3. .4. .0. .3. .3. .2. .0. .4
..3. .4. .2. .3. .2. .3. .4. .0. .2. .1. .2. .3. .3. .0. .3. .0
..0. .4. .0. .0. .1. .2. .2. .4. .4. .4. .4. .2. .4. .3. .1. .0
..4. .0. .3. .2. .1. .3. .3. .0. .1. .0. .2. .3. .2. .0. .0. .1
..3. .1. .1. .3. .4. .1. .1. .0. .2. .2. .4. .4. .0. .3. .2. .4
..1. .4. .2. .1. .2. .1. .2. .3. .4. .4. .2. .1. .2. .4. .3. .1

Crossrefs

Row 7 of A268944.

Sequence in context: A144350 A111216 A158672 * A276396 A291070 A004994

Adjacent sequences: A268945 A268946 A268947 * A268949 A268950 A268951

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved