A269587 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by more than one.

128, 1889, 13946, 67763, 248324, 745013, 1927694, 4453031, 9406088, 18482249, 34214498, 60251099, 101688716, 165466013, 260822774, 399829583, 597993104, 874942001, 1255198538, 1769040899, 2453461268, 3353224709, 4522033886

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 + 11*n^5 + 35*n^4 + 28*n^3 + 42*n^2 + 5*n - 1.

Conjectures from Colin Barker, Jan 24 2019: (Start)

G.f.: x*(128 + 865*x + 2418*x^2 + 1919*x^3 - 116*x^4 - 129*x^5 - 46*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:
..0. .0. .2. .1. .1. .2. .3. .0. .0. .0. .3. .3. .1. .0. .4. .4
..4. .3. .2. .2. .0. .2. .1. .4. .2. .0. .3. .1. .1. .3. .1. .0
..3. .1. .3. .4. .2. .4. .1. .2. .3. .0. .0. .4. .3. .2. .4. .1
..3. .0. .4. .4. .1. .3. .2. .3. .2. .1. .2. .3. .2. .2. .2. .0
..2. .4. .3. .2. .1. .1. .3. .1. .1. .1. .0. .0. .4. .2. .0. .0
..4. .4. .1. .3. .4. .4. .0. .4. .3. .1. .1. .0. .0. .1. .4. .0
..1. .2. .2. .0. .1. .2. .4. .1. .2. .1. .3. .1. .0. .0. .3. .0

Crossrefs

Row 7 of A269583.

Sequence in context: A269081 A200789 A250356 * A232053 A250234 A364690

Adjacent sequences: A269584 A269585 A269586 * A269588 A269589 A269590

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved