Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jan 10 2019 08:08:43
%S 5,12,29,66,137,261,463,775,1237,1898,2817,4064,5721,7883,10659,14173,
%T 18565,23992,30629,38670,48329,59841,73463,89475,108181,129910,155017,
%U 183884,216921,254567,297291,345593,400005,461092,529453,605722,690569
%N Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%H R. H. Hardin, <a href="/A266471/b266471.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (17/24)*n^3 - (25/24)*n^2 + (257/60)*n + 1.
%F Conjectures from _Colin Barker_, Jan 10 2019: (Start)
%F G.f.: x*(5 - 18*x + 32*x^2 - 28*x^3 + 11*x^4 - x^5) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0....0..0..0..0....0..1..1..1....0..0..0..0....0..0..1..1
%e ..0..0..0..0....0..0..0..0....1..0..0..0....0..0..1..1....0..1..0..0
%e ..1..1..1..1....0..0..0..0....1..0..1..1....1..1..0..0....1..0..0..0
%e ..1..1..1..1....1..1..1..1....1..1..0..0....1..1..1..1....1..1..1..1
%Y Row 4 of A266470.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2015