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A269603 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by one or less. 1
6, 36, 210, 1220, 7030, 40288, 229754, 1304934, 7385898, 41679780, 234601902, 1317558578, 7385249086, 41325945826, 230904832646, 1288466651340, 7181415415962, 39985405920156, 222432351559566, 1236355637246456 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Robert Israel, Maple-assisted proof for empirical recursion

FORMULA

Empirical: a(n) = 17*a(n-1) - 91*a(n-2) + 83*a(n-3) + 542*a(n-4) - 550*a(n-5) - 1651*a(n-6) - 745*a(n-7).

Empirical g.f.: 2*x*(3 - 33*x + 72*x^2 + 214*x^3 - 420*x^4 - 922*x^5 - 393*x^6) / ((1 - 5*x)*(1 - 12*x + 31*x^2 + 72*x^3 - 182*x^4 - 360*x^5 - 149*x^6)). - Colin Barker, Jan 24 2019

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

EXAMPLE

Some solutions for n=6:

..4. .4. .1. .3. .0. .3. .5. .1. .1. .5. .5. .1. .3. .0. .2. .0

..3. .5. .5. .2. .3. .1. .1. .3. .1. .5. .3. .2. .2. .0. .5. .3

..4. .3. .3. .1. .3. .5. .2. .2. .3. .2. .4. .1. .5. .2. .4. .5

..2. .2. .1. .3. .2. .1. .1. .0. .0. .5. .3. .4. .2. .3. .1. .0

..3. .5. .2. .0. .1. .3. .4. .4. .3. .2. .1. .0. .2. .1. .4. .4

..0. .1. .5. .3. .2. .3. .1. .4. .5. .2. .2. .2. .4. .3. .1. .4

MAPLE

T:= Matrix(42, 42):

for x from 0 to 5 do

  for v from 0 to 6 do

    i:= 1 + x + 6*v;

    for y in {$0..5} minus {x} do

      T[i, 1+y+6*v]:= 1;

    od:

    if abs(x-v) > 1 or v=6 then T[i, 1+x+6*x]:= 1 fi

od od:

u:= Vector([0$36, 1$6]): v:= Vector(42, 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

Column 5 of A269606.

Sequence in context: A269534 A269675 A269406 * A027910 A075848 A096979

Adjacent sequences:  A269600 A269601 A269602 * A269604 A269605 A269606

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2016

STATUS

approved

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Last modified September 26 13:50 EDT 2021. Contains 347668 sequences. (Running on oeis4.)