A269610 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by one or less.

14, 902, 10192, 58280, 229754, 714874, 1886252, 4405772, 9366790, 18476654, 34284584, 60459952, 102126002, 166254050, 262123204, 401850644, 600997502, 879255382, 1261218560, 1777246904, 2464424554, 3367619402, 4540648412

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 + 16*n^5 - 12*n^4 - 5*n^3 + 18*n^2 - 15*n + 4.

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

G.f.: 2*x*(7 + 395*x + 1684*x^2 + 608*x^3 - 321*x^4 + 143*x^5 + 6*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=4:
..1. .4. .2. .0. .2. .1. .4. .3. .1. .3. .4. .2. .4. .3. .3. .2
..4. .1. .0. .3. .4. .3. .2. .0. .3. .4. .1. .1. .1. .1. .4. .3
..0. .3. .3. .1. .1. .0. .4. .3. .1. .4. .4. .4. .0. .1. .2. .0
..1. .2. .2. .2. .1. .4. .0. .0. .0. .3. .2. .1. .3. .0. .4. .2
..1. .0. .0. .3. .3. .2. .1. .2. .2. .1. .2. .3. .4. .3. .3. .3
..4. .1. .3. .2. .3. .3. .4. .0. .1. .1. .4. .3. .4. .0. .2. .1
..4. .3. .1. .1. .2. .2. .0. .3. .1. .3. .1. .0. .3. .3. .1. .4

Crossrefs

Row 7 of A269606.

Sequence in context: A159871 A362998 A340259 * A115458 A241801 A337576

Adjacent sequences: A269607 A269608 A269609 * A269611 A269612 A269613

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved