A268943 Number of length-n 0..7 arrays with no repeated value unequal to the previous repeated value plus one mod 7+1.

8, 64, 504, 3928, 30344, 232696, 1773384, 13443064, 101433800, 762265720, 5707893576, 42605289208, 317113497800, 2354253598072, 17437541654088, 128885063291896, 950791205063624, 7001691181273720, 51477520840048968

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 34*a(n-2) - 56*a(n-3).

Conjectures from Colin Barker, Jan 17 2019: (Start)

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

a(n) = (-272*7^n + (153-37*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(153+37*sqrt(17))) / 34.

(End)

Example

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

Crossrefs

Column 7 of A268944.

Sequence in context: A267231 A267470 A227591 * A269639 A269536 A269677

Adjacent sequences: A268940 A268941 A268942 * A268944 A268945 A268946

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved