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A267243 Number of n X 6 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing. 1
7, 50, 475, 6292, 107015, 2093467, 43555569, 924051709, 19614050515, 413556580944, 8645774602327, 179276181587698, 3691120876565687, 75550095426967737, 1538986699132717645, 31229753343696948035 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 6 of A267245.

LINKS

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

Robert Israel, Maple-assisted proof of empirical recurrence

FORMULA

Empirical: a(n) = 114*a(n-1) - 5915*a(n-2) + 186008*a(n-3) - 3982785*a(n-4) + 61835542*a(n-5) - 723657627*a(n-6) + 6549515604*a(n-7) - 46652032035*a(n-8) + 264676225246*a(n-9) - 1205477853945*a(n-10) + 4427867737616*a(n-11) - 13139368875011*a(n-12) + 31468929403866*a(n-13) - 60602488003009*a(n-14) + 93197329064964*a(n-15) - 113220771193368*a(n-16) + 106920682204032*a(n-17) - 76630180181904*a(n-18) + 40173465734208*a(n-19) - 14497964755200*a(n-20) + 3213273369600*a(n-21) - 329204736000*a(n-22).

Empirical formula verified (see link). - Robert Israel, Sep 08 2019

EXAMPLE

Some solutions for n=4:

  0 0 0 0 1 1   0 0 0 0 1 1   0 0 0 0 1 1   0 0 0 1 1 1

  0 0 0 1 0 1   0 0 1 1 0 0   0 0 1 1 0 0   0 1 1 0 0 1

  0 1 1 1 1 0   0 0 0 1 1 1   0 1 0 0 0 1   1 1 1 1 1 0

  0 0 1 1 1 1   0 1 0 1 0 1   1 1 0 1 0 1   1 0 1 1 1 1

MAPLE

S[2]:= [[0, 0, 0], [0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 0], [1, 1, 1]]:

for i from 3 to 6 do

  S[i]:= map(proc(t) [op(t[1..i-1]), t[i-1], op(t[i..-1]), 0], [op(t[1..i-1]), t[i-1], op(t[i..-1]), 1],

     [op(t[1..i-1]), 1-t[i-1], op(t[i..-1]), 1] end proc, S[i-1])

od:

states:= S[6]:

T:= Matrix(486, 486, proc(i, j) local k;

  if add(states[j, k]-states[i, k], k=1..6) > 0 then return 0 fi;

  for k from 7 to 11 do if states[j, k]>states[i, k] then return 0 fi od;

  for k from 1 to 5 do if states[i, k]>=states[i, k+1] and states[j, k+6]<>states[i, k+6] then return 0 fi od;

1

end proc):

E:= Vector(486): E[1]:= 1:

U[0]:= Vector[row](486, 1):

for k from 1 to 25 do U[k]:= U[k-1].T od:

seq(U[j] . E, j=1..25); # Robert Israel, Sep 08 2019

CROSSREFS

Cf. A267245.

Sequence in context: A005460 A053155 A266432 * A197570 A319884 A204463

Adjacent sequences:  A267240 A267241 A267242 * A267244 A267245 A267246

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 12 2016

STATUS

approved

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Last modified August 11 04:00 EDT 2020. Contains 336421 sequences. (Running on oeis4.)