A269466 Number of length-n 0..7 arrays with no repeated value equal to the previous repeated value.

8, 64, 504, 3976, 31304, 246232, 1934856, 15190840, 119174216, 934305400, 7320389832, 57325443448, 448697920328, 3510562344184, 27455875247304, 214658236385656, 1677757456358984, 13109740539632632, 102412911071378376

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) -28*a(n-2) -98*a(n-3).

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

G.f.: 8*x*(1 - 5*x - 13*x^2) / ((1 - 7*x)*(1 - 6*x - 14*x^2)).

a(n) = 2*(-92*7^n + (345-67*sqrt(23))*(3-sqrt(23))^n + (3+sqrt(23))^n*(345+67*sqrt(23))) / 1127.

(End)

Example

Some solutions for n=5:
..7. .5. .3. .6. .4. .7. .3. .6. .3. .0. .1. .7. .7. .7. .3. .1
..5. .7. .0. .4. .3. .6. .5. .5. .5. .4. .7. .1. .4. .7. .2. .1
..3. .5. .7. .3. .5. .1. .2. .7. .5. .7. .4. .0. .6. .1. .7. .7
..6. .4. .5. .2. .3. .1. .4. .6. .0. .3. .5. .7. .5. .4. .0. .1
..6. .0. .0. .1. .6. .4. .3. .3. .4. .2. .4. .0. .4. .5. .7. .4

Crossrefs

Column 7 of A269467.

Sequence in context: A269677 A269408 A269605 * A127426 A268456 A126629

Adjacent sequences: A269463 A269464 A269465 * A269467 A269468 A269469

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved