A267242 Number of nX5 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.

6, 34, 232, 1986, 20040, 220235, 2499080, 28501471, 323067002, 3626695952, 40306404192, 443852375808, 4848323701804, 52590398731297, 567018802063680, 6081537709403509, 64929807220896558, 690446673537426382

Offset

1,1

Comments

Column 5 of A267245.

Links

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

Robert Israel, Maple-assisted proof of empirical formula

Index entries for linear recurrences with constant coefficients, signature (52, -1196, 16140, -142918, 879116, -3875668, 12442580, -29232481, 50015232, -61355336, 52355680, -29405200, 9744000, -1440000).

Formula

Empirical: a(n) = 52*a(n-1) -1196*a(n-2) +16140*a(n-3) -142918*a(n-4) +879116*a(n-5) -3875668*a(n-6) +12442580*a(n-7) -29232481*a(n-8) +50015232*a(n-9) -61355336*a(n-10) +52355680*a(n-11) -29405200*a(n-12) +9744000*a(n-13) -1440000*a(n-14).

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

Example

Some solutions for n=4
..0..0..0..0..1....0..0..0..1..1....0..0..0..1..1....0..0..0..0..1
..0..0..0..1..0....0..1..1..0..0....0..1..1..0..0....0..0..0..1..0
..0..1..1..0..0....0..0..1..1..1....1..1..1..0..1....0..0..0..0..1
..1..0..1..1..1....1..0..1..0..1....1..1..1..1..0....0..1..1..1..0

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 5 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[5]:
T:= Matrix(162, 162, proc(i, j) local k;
  if add(states[j, k]-states[i, k], k=1..5) > 0 then return 0 fi;
  for k from 6 to 9 do if states[j, k]>states[i, k] then return 0 fi od;
  for k from 1 to 4 do if states[i, k]>=states[i, k+1] and states[j, k+5]<>states[i, k+5] then return 0 fi od;
1
end proc):
E:= Vector(162): E[1]:= 1:
U[0]:= Vector[row](162, 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: A216317 A370324 A230331 * A197436 A334787 A302148

Adjacent sequences: A267239 A267240 A267241 * A267243 A267244 A267245

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved