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A267241 Number of nX4 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing. 1
5, 22, 105, 567, 3351, 20676, 129129, 804817, 4982759, 30629206, 187121865, 1137631979, 6891047527, 41628865000, 250987078681, 1511105743781, 9088662549303, 54625229882746, 328144877989145, 1970524978549951 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 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) = 24*a(n-1) -246*a(n-2) +1420*a(n-3) -5121*a(n-4) +12084*a(n-5) -18944*a(n-6) +19536*a(n-7) -12720*a(n-8) +4736*a(n-9) -768*a(n-10).

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

EXAMPLE

Some solutions for n=4

..0..0..0..0....0..0..0..0....0..0..1..1....0..0..1..1....0..0..0..1

..0..0..0..0....0..0..0..1....0..0..1..1....0..1..0..1....0..1..1..0

..0..1..1..1....0..1..1..0....0..1..1..1....1..0..1..0....0..1..1..1

..1..0..1..1....0..1..1..0....1..0..1..1....1..0..1..0....0..1..1..1

MAPLE

states:= select(proc(x) (x[1]=x[2] or x[5]=1) and (x[2]=x[3] or x[6]=1) and (x[3]=x[4] or x[7]=1) end proc, [seq(seq(seq(seq(seq(seq(seq([a, b, c, d, e, f, g], g=0..1), f=0..1), e=0..1), d=0..1), c=0..1), b=0..1), a=0..1)]):

T:= Matrix(54, 54, proc(i, j) local k;

  if add(states[j, k]-states[i, k], k=1..4) > 0 then return 0 fi;

  if states[j, 5]>states[i, 5] or states[j, 6]>states[i, 6] or states[j, 7]>states[i, 7] then return 0 fi;

  if states[i, 1]>=states[i, 2] and states[j, 5]<> states[i, 5] then return 0 fi;

  if states[i, 2]>=states[i, 3] and states[j, 6]<> states[i, 6] then return 0 fi;

  if states[i, 3]>=states[i, 4] and states[j, 7]<> states[i, 7] then return 0 fi;

1

end proc):

U:= Vector(54, 1):

E[0]:= Vector(54): E[0][1]:= 1:

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

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

CROSSREFS

Cf. A267245.

Sequence in context: A008485 A213684 A082297 * A162271 A164593 A153789

Adjacent sequences:  A267238 A267239 A267240 * A267242 A267243 A267244

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 12 2016

STATUS

approved

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Last modified August 10 01:21 EDT 2020. Contains 336360 sequences. (Running on oeis4.)