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

%I A267242 #10 Mar 17 2024 11:15:02
%S A267242 6,34,232,1986,20040,220235,2499080,28501471,323067002,3626695952,
%T A267242 40306404192,443852375808,4848323701804,52590398731297,
%U A267242 567018802063680,6081537709403509,64929807220896558,690446673537426382
%N A267242 Number of nX5 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.
%C A267242 Column 5 of A267245.
%H A267242 R. H. Hardin, <a href="/A267242/b267242.txt">Table of n, a(n) for n = 1..210</a>
%H A267242 Robert Israel, <a href="/A267242/a267242.pdf">Maple-assisted proof of empirical formula</a>
%H A267242 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (52, -1196, 16140, -142918, 879116, -3875668, 12442580, -29232481, 50015232, -61355336, 52355680, -29405200, 9744000, -1440000).
%F A267242 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).
%F A267242 Empirical formula verified (see link). - _Robert Israel_, Sep 08 2019
%e A267242 Some solutions for n=4
%e A267242 ..0..0..0..0..1....0..0..0..1..1....0..0..0..1..1....0..0..0..0..1
%e A267242 ..0..0..0..1..0....0..1..1..0..0....0..1..1..0..0....0..0..0..1..0
%e A267242 ..0..1..1..0..0....0..0..1..1..1....1..1..1..0..1....0..0..0..0..1
%e A267242 ..1..0..1..1..1....1..0..1..0..1....1..1..1..1..0....0..1..1..1..0
%p A267242 S[2]:= [[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]:
%p A267242 for i from 3 to 5 do
%p A267242   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],
%p A267242      [op(t[1..i-1]),1-t[i-1],op(t[i..-1]),1] end proc, S[i-1])
%p A267242 od:
%p A267242 states:= S[5]:
%p A267242 T:= Matrix(162,162,proc(i,j) local k;
%p A267242   if add(states[j,k]-states[i,k],k=1..5) > 0 then return 0 fi;
%p A267242   for k from 6 to 9 do if states[j,k]>states[i,k] then return 0 fi od;
%p A267242   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;
%p A267242 1
%p A267242 end proc):
%p A267242 E:= Vector(162): E[1]:= 1:
%p A267242 U[0]:= Vector[row](162,1):
%p A267242 for k from 1 to 25 do U[k]:= U[k-1].T od:
%p A267242 seq(U[j] . E, j=1..25); # _Robert Israel_, Sep 08 2019
%Y A267242 Cf. A267245.
%K A267242 nonn
%O A267242 1,1
%A A267242 _R. H. Hardin_, Jan 12 2016