|
%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
|
