A269540 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than one.

22, 418, 2878, 12214, 38878, 102202, 234358, 485038, 926854, 1661458, 2826382, 4602598, 7222798, 10980394, 16239238, 23444062, 33131638, 45942658, 62634334, 84093718, 111351742, 145597978, 188196118, 240700174, 304871398, 382695922

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 + 5*n^4 + 12*n^3 - 6*n^2 + 6*n - 2.

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

G.f.: 2*x*(11 + 132*x + 207*x^2 + 38*x^3 - 21*x^4 - 6*x^5 - x^6) / (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>7.

(End)

Example

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

Crossrefs

Row 6 of A269537.

Sequence in context: A049663 A246645 A183539 * A095219 A299320 A014904

Adjacent sequences: A269537 A269538 A269539 * A269541 A269542 A269543

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved