A269465 Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.

7, 49, 336, 2310, 15834, 108402, 741090, 5060706, 34523202, 235304034, 1602555906, 10906971810, 74188793154, 504367206882, 3427339028610, 23280526483746, 158079249910722, 1073053862250594, 7281968079533826, 49404973360789410

Offset

1,1

Links

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

Formula

Empirical: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3).

Conjectures from Colin Barker, Jan 22 2019: (Start)

G.f.: 7*x*(1 - 4*x - 11*x^2) / ((1 - 6*x)*(1 - 5*x - 12*x^2)).

a(n) = (7/657)*2^(-4-n) * (-73*3^n*4^(1+n) + (949-103*sqrt(73))*(5-sqrt(73))^n + (5+sqrt(73))^n*(949+103*sqrt(73))).

(End)

Example

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

Crossrefs

Column 6 of A269467.

Sequence in context: A269676 A269407 A269604 * A268455 A323559 A366925

Adjacent sequences: A269462 A269463 A269464 * A269466 A269467 A269468

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved