A269686 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 4+1.

5, 25, 125, 615, 2995, 14465, 69405, 331255, 1574195, 7454385, 35195485, 165766535, 779138355, 3655796065, 17128371485, 80151962775, 374677320115, 1749902587025, 8166591981405, 38087874378535, 177538468225715, 827166275107905

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 13*a(n-2) - 12*a(n-3).

Conjectures from Colin Barker, Jan 27 2019: (Start)

G.f.: 5*x*(1 - 3*x - 2*x^2) / ((1 - 4*x)*(1 - 4*x - 3*x^2)).

a(n) = (-5/42)*(7*4^n + (2-sqrt(7))^n*(-7+3*sqrt(7)) - (2+sqrt(7))^n*(7+3*sqrt(7))).

(End)

Example

Some solutions for n=7:
..3. .0. .4. .1. .2. .2. .2. .3. .2. .3. .3. .0. .0. .2. .2. .3
..1. .3. .2. .3. .4. .0. .3. .0. .2. .1. .4. .0. .2. .2. .0. .3
..2. .0. .3. .0. .0. .1. .1. .2. .2. .0. .1. .4. .2. .2. .3. .4
..2. .4. .2. .2. .3. .1. .1. .1. .2. .0. .0. .1. .2. .3. .0. .2
..2. .3. .3. .1. .0. .0. .1. .3. .4. .0. .0. .0. .4. .4. .3. .3
..2. .3. .2. .4. .2. .1. .3. .2. .2. .2. .2. .2. .3. .0. .2. .2
..1. .3. .3. .0. .3. .2. .4. .4. .1. .3. .4. .4. .1. .4. .0. .4

Crossrefs

Column 4 of A269690.

Sequence in context: A269615 A269579 A269431 * A269490 A370144 A269772

Adjacent sequences: A269683 A269684 A269685 * A269687 A269688 A269689

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved