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A267242 Number of nX5 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing. 1
6, 34, 232, 1986, 20040, 220235, 2499080, 28501471, 323067002, 3626695952, 40306404192, 443852375808, 4848323701804, 52590398731297, 567018802063680, 6081537709403509, 64929807220896558, 690446673537426382 (list; graph; refs; listen; history; text; internal format)
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

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: A184185 A216317 A230331 * A197436 A334787 A302148

Adjacent sequences:  A267239 A267240 A267241 * A267243 A267244 A267245

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 12 2016

STATUS

approved

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Last modified August 10 02:02 EDT 2020. Contains 336365 sequences. (Running on oeis4.)