A267241 Number of nX4 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.

5, 22, 105, 567, 3351, 20676, 129129, 804817, 4982759, 30629206, 187121865, 1137631979, 6891047527, 41628865000, 250987078681, 1511105743781, 9088662549303, 54625229882746, 328144877989145, 1970524978549951

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

Index entries for linear recurrences with constant coefficients, signature (24, -246, 1420, -5121, 12084, -18944, 19536, -12720, 4736, -768).

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

Mathematica

LinearRecurrence[{24, -246, 1420, -5121, 12084, -18944, 19536, -12720, 4736, -768}, {5, 22, 105, 567, 3351, 20676, 129129, 804817, 4982759, 30629206, 187121865}, 25] (* Jean-François Alcover, Oct 25 2022, after Robert Israel *)

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