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A266471 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

%I A266471 #8 Jan 10 2019 08:08:43
%S A266471 5,12,29,66,137,261,463,775,1237,1898,2817,4064,5721,7883,10659,14173,
%T A266471 18565,23992,30629,38670,48329,59841,73463,89475,108181,129910,155017,
%U A266471 183884,216921,254567,297291,345593,400005,461092,529453,605722,690569
%N A266471 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%H A266471 R. H. Hardin, <a href="/A266471/b266471.txt">Table of n, a(n) for n = 1..210</a>
%F A266471 Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (17/24)*n^3 - (25/24)*n^2 + (257/60)*n + 1.
%F A266471 Conjectures from _Colin Barker_, Jan 10 2019: (Start)
%F A266471 G.f.: x*(5 - 18*x + 32*x^2 - 28*x^3 + 11*x^4 - x^5) / (1 - x)^6.
%F A266471 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 A266471 (End)
%e A266471 Some solutions for n=4:
%e A266471 ..0..0..0..0....0..0..0..0....0..1..1..1....0..0..0..0....0..0..1..1
%e A266471 ..0..0..0..0....0..0..0..0....1..0..0..0....0..0..1..1....0..1..0..0
%e A266471 ..1..1..1..1....0..0..0..0....1..0..1..1....1..1..0..0....1..0..0..0
%e A266471 ..1..1..1..1....1..1..1..1....1..1..0..0....1..1..1..1....1..1..1..1
%Y A266471 Row 4 of A266470.
%K A266471 nonn
%O A266471 1,1
%A A266471 _R. H. Hardin_, Dec 29 2015