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

1,1

Comments

Column 7 of A269606.

Links

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

Robert Israel, Maple-assisted proof of empirical recursion

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

Example

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

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

Crossrefs

Cf. A269606.

Sequence in context: A269536 A269677 A269408 * A269466 A127426 A268456

Adjacent sequences: A269602 A269603 A269604 * A269606 A269607 A269608

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved