A269692 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by plus or minus one modulo n+1.

40, 525, 3544, 14465, 44556, 114205, 256880, 523809, 989380, 1757261, 2967240, 4802785, 7499324, 11353245, 16731616, 24082625, 33946740, 46968589, 63909560, 85661121, 113258860, 147897245, 190945104, 243961825, 308714276, 387194445

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 8*n^3 - 7*n^2 - 4*n + 1 for n>1.

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

G.f.: x*(40 + 245*x + 709*x^2 - 718*x^3 + 750*x^4 - 427*x^5 + 141*x^6 - 20*x^7) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>8.

(End)

Example

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

Crossrefs

Row 6 of A269690.

Sequence in context: A069079 A093744 A109105 * A247409 A107419 A159946

Adjacent sequences: A269689 A269690 A269691 * A269693 A269694 A269695

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved