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A269605 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by one or less. 1
8, 64, 504, 3962, 31024, 242226, 1886252, 14654952, 113629480, 879470154, 6796127732, 52443005888, 404170590152, 3111359345068, 23927329547328, 183840499514208, 1411335451447128, 10826702362761906, 82998453154738884 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 3 02:07 EDT 2022. Contains 355029 sequences. (Running on oeis4.)