|
%I #7 Aug 24 2018 08:52:33
%S 8,27,54,96,157,241,352,494,671,887,1146,1452,1809,2221,2692,3226,
%T 3827,4499,5246,6072,6981,7977,9064,10246,11527,12911,14402,16004,
%U 17721,19557,21516,23602,25819,28171,30662,33296,36077,39009,42096,45342,48751,52327
%N Number of 3 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C Row 3 of A223949.
%H R. H. Hardin, <a href="/A223950/b223950.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (2/3)*n^3 + (3/2)*n^2 + (41/6)*n + 2 for n>1.
%F Conjectures from _Colin Barker_, Aug 24 2018: (Start)
%F G.f.: x*(8 - 5*x - 6*x^2 + 10*x^3 - 3*x^4) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F (End)
%e Some solutions for n=3:
%e ..1..1..1....0..1..1....0..0..1....0..0..1....0..0..0....0..0..0....0..0..0
%e ..1..1..1....0..1..1....0..0..0....1..1..1....0..0..1....1..1..1....1..1..1
%e ..0..1..1....1..1..1....0..0..1....0..0..0....0..1..1....0..0..1....1..1..1
%Y Cf. A223949.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 29 2013
|
