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

Author

R. H. Hardin, Jan 12 2016

Keywords

• nonn

Comments

Column 4 of A267245.

Examples

			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
		

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).

Crossrefs

Cf. A267245.

Programs

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 *)

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