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A269604 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by one or less. 1
7, 49, 336, 2298, 15630, 105892, 714874, 4811578, 32300252, 216337084, 1446056046, 9648789758, 64281141440, 427655897226, 2841661493142, 18861464959350, 125070420653458, 828618463551536, 5485481885293294, 36288577806336542 (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 of empirical recursion

FORMULA

Empirical: a(n) = 26*a(n-1) - 243*a(n-2) + 833*a(n-3) + 567*a(n-4) - 7567*a(n-5) - 1006*a(n-6) + 27361*a(n-7) + 31306*a(n-8) + 9984*a(n-9).

Empirical g.f.: x*(7 - 133*x + 763*x^2 - 362*x^3 - 7256*x^4 + 3224*x^5 + 32851*x^6 + 34133*x^7 + 10511*x^8) / ((1 - 6*x)*(1 - 20*x + 123*x^2 - 95*x^3 - 1137*x^4 + 745*x^5 + 5476*x^6 + 5495*x^7 + 1664*x^8)). - Colin Barker, Jan 24 2019

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

EXAMPLE

Some solutions for n=6:

..3. .2. .6. .1. .5. .1. .2. .5. .2. .6. .4. .0. .1. .5. .5. .4

..6. .0. .3. .2. .0. .1. .3. .2. .3. .1. .3. .5. .4. .4. .4. .0

..6. .1. .6. .3. .1. .4. .6. .4. .1. .2. .1. .0. .5. .0. .3. .3

..2. .4. .4. .6. .4. .6. .2. .6. .3. .4. .3. .0. .3. .1. .6. .5

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

..5. .1. .0. .4. .2. .0. .4. .1. .1. .1. .4. .6. .6. .6. .0. .2

MAPLE

with(LinearAlgebra):

T:= Matrix(56, 56):

for x from 0 to 6 do

  for v from 0 to 7 do

    i:= 1 + x + 7*v;

    for y in {$0..6} minus {x} do

      T[i, 1+y+7*v]:= 1;

    od:

    if abs(x-v) > 1 or v=7 then T[i, 1+x+7*x]:= 1 fi

od od:

u:= Vector([0$49, 1$7]): v:= Vector(56, 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 6 of A269606.

Sequence in context: A269535 A269676 A269407 * A269465 A268455 A323559

Adjacent sequences:  A269601 A269602 A269603 * A269605 A269606 A269607

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2016

STATUS

approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)