A269605 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by one or less.

8, 64, 504, 3962, 31024, 242226, 1886252, 14654952, 113629480, 879470154, 6796127732, 52443005888, 404170590152, 3111359345068, 23927329547328, 183840499514208, 1411335451447128, 10826702362761906, 82998453154738884

Offset: 1

Author

R. H. Hardin, Mar 01 2016

Keywords

• nonn

Comments

Column 7 of A269606.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of empirical recursion

Crossrefs

Cf. A269606.

Programs

Maple

with(LinearAlgebra):
T:= Matrix(72,72):
for x from 0 to 7 do
  for v from 0 to 8 do
    i:= 1 + x + 8*v;
    for y in {$0..7} minus {x} do
      T[i,1+y+8*v]:= 1;
    od:
    if abs(x-v) > 1 or v=8 then T[i,1+x+8*x]:= 1 fi
od od:
u:= Vector([0$64,1$8]): v:= Vector(72,1):
Tv[1]:= v:
for n from 2 to 50 do Tv[n]:= T . Tv[n-1] od:
seq(u^%T . Tv[n], n=1..50); # Robert Israel, Jan 24 2019

Formula

Empirical: a(n) = 31*a(n-1) -353*a(n-2) +1601*a(n-3) -435*a(n-4) -14505*a(n-5) +7118*a(n-6) +65542*a(n-7) +66279*a(n-8) +19971*a(n-9)

Empirical formula verified: see link. - Robert Israel, Jan 24 2019