A269644 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

20, 969, 9928, 55225, 216528, 675151, 1789528, 4200933, 8974480, 17780443, 33120936, 58606993, 99291088, 162060135, 256094008, 393394621, 589390608, 863622643, 1240514440, 1750234473, 2429653456, 3323402623, 4485037848

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 - 22*n^3 + 28*n^2 - 37*n + 13 for n>2.

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

G.f.: x*(20 + 809*x + 2736*x^2 + 1813*x^3 - 152*x^4 - 31*x^5 - 240*x^6 + 123*x^7 - 44*x^8 + 6*x^9) / (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>10.

(End)

Example

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

Crossrefs

Row 7 of A269640.

Sequence in context: A269413 A274764 A069578 * A349964 A347856 A128482

Adjacent sequences: A269641 A269642 A269643 * A269645 A269646 A269647

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved