A269635 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

4, 16, 60, 221, 796, 2828, 9928, 34537, 119236, 409098, 1396288, 4744671, 16062116, 54199810, 182382428, 612236251, 2050883956, 6857469364, 22892085300, 76311433969, 254067536796, 844941922160, 2807225267056, 9318543171653

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 21*a(n-2) - 19*a(n-3) + 93*a(n-4) + 27*a(n-5) - 133*a(n-6) - 87*a(n-7).

Empirical g.f.: x*(4 - 20*x + 93*x^3 - x^4 - 151*x^5 - 89*x^6) / ((1 - 3*x)*(1 - 6*x + 3*x^2 + 28*x^3 - 9*x^4 - 54*x^5 - 29*x^6)). - Colin Barker, Jan 25 2019

Example

Some solutions for n=9:
..2. .1. .2. .1. .2. .0. .2. .1. .1. .1. .1. .3. .3. .0. .0. .2
..0. .2. .3. .3. .2. .1. .0. .3. .3. .2. .3. .0. .1. .2. .2. .0
..3. .0. .0. .0. .1. .3. .0. .2. .2. .2. .0. .1. .3. .0. .1. .3
..1. .3. .2. .1. .0. .2. .1. .3. .1. .0. .3. .1. .0. .1. .3. .1
..0. .0. .2. .1. .3. .0. .0. .2. .3. .2. .1. .0. .3. .2. .0. .2
..1. .1. .0. .2. .2. .2. .2. .0. .2. .3. .2. .3. .0. .1. .3. .3
..3. .3. .3. .0. .3. .3. .2. .1. .0. .1. .0. .2. .0. .2. .2. .1
..0. .3. .2. .1. .1. .2. .1. .2. .1. .3. .2. .0. .2. .3. .0. .0
..0. .0. .0. .0. .2. .0. .3. .1. .0. .1. .2. .2. .0. .2. .3. .2

Crossrefs

Column 3 of A269640.

Sequence in context: A255303 A273347 A268939 * A267928 A269532 A269673

Adjacent sequences: A269632 A269633 A269634 * A269636 A269637 A269638

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved