A269581 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by more than one.

7, 49, 343, 2371, 16237, 110339, 745013, 5003189, 33444515, 222678103, 1477520701, 9774231593, 64488659975, 424492364229, 2788409406459, 18282749345115, 119676718166685, 782230745611877, 5106010760180351, 33289477289878243

Offset

1,1

Links

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

Formula

Empirical: a(n) = 30*a(n-1) - 356*a(n-2) + 2064*a(n-3) - 5618*a(n-4) + 4356*a(n-5) + 4964*a(n-6) + 480*a(n-7) - 143*a(n-8) - 6*a(n-9).

Empirical g.f.: x*(7 - 161*x + 1365*x^2 - 4923*x^3 + 5405*x^4 + 4143*x^5 + 253*x^6 - 111*x^7 - 4*x^8) / ((1 - 6*x)*(1 - 24*x + 212*x^2 - 792*x^3 + 866*x^4 + 840*x^5 + 76*x^6 - 24*x^7 - x^8)). Colin Barker, Jan 24 2019

Example

Some solutions for n=6:
..3. .0. .0. .3. .5. .4. .6. .1. .2. .5. .4. .3. .1. .0. .0. .3
..6. .3. .0. .0. .0. .3. .3. .5. .1. .5. .4. .5. .0. .0. .1. .6
..3. .5. .1. .5. .3. .4. .3. .2. .0. .1. .3. .2. .0. .1. .1. .1
..3. .2. .3. .6. .6. .1. .5. .3. .0. .6. .1. .0. .2. .0. .1. .3
..0. .6. .5. .3. .6. .0. .6. .6. .6. .2. .5. .0. .0. .2. .2. .1
..4. .4. .0. .0. .1. .4. .3. .0. .0. .4. .1. .2. .0. .5. .5. .3

Crossrefs

Column 6 of A269583.

Sequence in context: A228738 A057845 A269617 * A269433 A269688 A269492

Adjacent sequences: A269578 A269579 A269580 * A269582 A269583 A269584

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved